LMFDB - Embedded newform 210.2.u.b.103.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(73,210)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("210.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.u (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.4
Root			$0.277956 + 0.213283i$ of defining polynomial
Character	$\chi$	$=$	210.103
Dual form			210.2.u.b.157.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.14315 - 0.637899i) q^{5} -1.00000i q^{6} +(0.153213 + 2.64131i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.14315 - 0.637899i) q^{5} -1.00000i q^{6} +(0.153213 + 2.64131i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.17085 + 1.90502i) q^{10} +(2.27722 + 3.94427i) q^{11} +(0.965926 - 0.258819i) q^{12} +(1.77772 - 1.77772i) q^{13} +(-2.51166 + 0.831614i) q^{14} +(-2.23522 + 0.0614757i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.06747 + 3.98386i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(1.88956 - 3.27281i) q^{19} +(-1.53707 + 1.62401i) q^{20} +(0.535629 - 2.59097i) q^{21} +(-3.22048 + 3.22048i) q^{22} +(-7.77857 + 2.08426i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.18617 - 2.73423i) q^{25} +(2.17725 + 1.25704i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.45334 - 2.21084i) q^{28} -1.55563i q^{29} +(-0.637899 - 2.14315i) q^{30} +(3.37208 - 1.94687i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.17878 - 4.39926i) q^{33} -4.12440 q^{34} +(2.01325 + 5.56299i) q^{35} -1.00000 q^{36} +(-2.95980 - 11.0461i) q^{37} +(3.65035 + 0.978107i) q^{38} +(-2.17725 + 1.25704i) q^{39} +(-1.96650 - 1.06437i) q^{40} -11.3796i q^{41} +(2.64131 - 0.153213i) q^{42} +(0.367260 + 0.367260i) q^{43} +(-3.94427 - 2.27722i) q^{44} +(2.17497 + 0.519137i) q^{45} +(-4.02648 - 6.97408i) q^{46} +(4.87829 - 1.30713i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-6.95305 + 0.809365i) q^{49} +(3.72452 + 3.33586i) q^{50} +(2.06220 - 3.57183i) q^{51} +(-0.650691 + 2.42841i) q^{52} +(-2.18307 + 8.14732i) q^{53} +(0.500000 - 0.866025i) q^{54} +(7.39647 + 7.00051i) q^{55} +(1.75935 - 1.97603i) q^{56} +(-2.67224 + 2.67224i) q^{57} +(1.50262 - 0.402626i) q^{58} +(-0.221511 - 0.383668i) q^{59} +(1.90502 - 1.17085i) q^{60} +(7.09442 + 4.09597i) q^{61} +(2.75329 + 2.75329i) q^{62} +(-1.18797 + 2.36405i) q^{63} +1.00000i q^{64} +(2.67591 - 4.94392i) q^{65} +(3.94427 - 2.27722i) q^{66} +(-8.99808 - 2.41103i) q^{67} +(-1.06747 - 3.98386i) q^{68} +8.05297 q^{69} +(-4.85237 + 3.38446i) q^{70} -6.68403 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-4.20080 - 1.12560i) q^{73} +(9.90370 - 5.71790i) q^{74} +(-4.75120 + 1.55760i) q^{75} +3.77912i q^{76} +(-10.0691 + 6.61917i) q^{77} +(-1.77772 - 1.77772i) q^{78} +(-4.08283 - 2.35722i) q^{79} +(0.519137 - 2.17497i) q^{80} +(0.500000 + 0.866025i) q^{81} +(10.9919 - 2.94527i) q^{82} +(-3.21718 + 3.21718i) q^{83} +(0.831614 + 2.51166i) q^{84} +(0.253550 + 9.21894i) q^{85} +(-0.259692 + 0.449799i) q^{86} +(-0.402626 + 1.50262i) q^{87} +(1.17878 - 4.39926i) q^{88} +(3.02425 - 5.23816i) q^{89} +(0.0614757 + 2.23522i) q^{90} +(4.96788 + 4.42314i) q^{91} +(5.69431 - 5.69431i) q^{92} +(-3.76106 + 1.00777i) q^{93} +(2.52519 + 4.37376i) q^{94} +(1.96188 - 8.21947i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(0.462652 + 0.462652i) q^{97} +(-2.58137 - 6.50665i) q^{98} +4.55445i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 - 4 * q^7	$ 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28} - 4 q^{30} - 24 q^{31} + 4 q^{33} - 16 q^{34} - 44 q^{35} - 16 q^{36} - 8 q^{37} - 20 q^{38} + 12 q^{39} + 8 q^{42} - 24 q^{43} - 4 q^{45} - 4 q^{46} - 52 q^{49} + 8 q^{51} + 8 q^{52} - 28 q^{53} + 8 q^{54} + 56 q^{55} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} + 16 q^{65} - 84 q^{67} + 12 q^{68} + 8 q^{69} + 4 q^{70} - 32 q^{71} + 16 q^{73} + 24 q^{74} - 24 q^{75} + 44 q^{77} - 16 q^{78} - 12 q^{79} + 12 q^{80} + 8 q^{81} + 36 q^{82} + 16 q^{83} - 4 q^{84} + 8 q^{85} - 8 q^{86} + 48 q^{87} - 4 q^{88} + 16 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 8 q^{94} + 72 q^{95} - 44 q^{97} + 24 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	2.14315	−	0.637899i	0.958445	−	0.285277i
$5$	2.14315	−	0.637899i	0.958445	−	0.285277i
$6$		−	1.00000i		−	0.408248i
$7$	0.153213	+	2.64131i	0.0579090	+	0.998322i
$7$	0.153213	+	2.64131i	0.0579090	+	0.998322i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	1.17085	+	1.90502i	0.370256	+	0.602421i
$11$	2.27722	+	3.94427i	0.686609	+	1.18924i	0.972928	+	0.231107i	$0.0742348\pi$
$11$	2.27722	+	3.94427i	0.686609	+	1.18924i	−0.286319	+	0.958134i	$0.592432\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	1.77772	−	1.77772i	0.493051	−	0.493051i	−0.416215	−	0.909266i	$-0.636644\pi$
$13$	1.77772	−	1.77772i	0.493051	−	0.493051i	0.909266	+	0.416215i	$0.136644\pi$
$14$	−2.51166	+	0.831614i	−0.671268	+	0.222258i
$15$	−2.23522	+	0.0614757i	−0.577132	+	0.0158730i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.06747	+	3.98386i	−0.258900	+	0.966228i	0.706979	+	0.707234i	$0.250057\pi$
$17$	−1.06747	+	3.98386i	−0.258900	+	0.966228i	−0.965879	+	0.258993i	$0.916609\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	1.88956	−	3.27281i	0.433494	−	0.750834i	−0.563677	−	0.825995i	$-0.690614\pi$
$19$	1.88956	−	3.27281i	0.433494	−	0.750834i	0.997171	+	0.0751610i	$0.0239471\pi$
$20$	−1.53707	+	1.62401i	−0.343700	+	0.363140i
$21$	0.535629	−	2.59097i	0.116884	−	0.565395i
$22$	−3.22048	+	3.22048i	−0.686609	+	0.686609i
$23$	−7.77857	+	2.08426i	−1.62194	+	0.434599i	−0.951572	−	0.307426i	$-0.900532\pi$
$23$	−7.77857	+	2.08426i	−1.62194	+	0.434599i	−0.670372	+	0.742025i	$0.733866\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.18617	−	2.73423i	0.837234	−	0.546845i
$26$	2.17725	+	1.25704i	0.426995	+	0.246525i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.45334	−	2.21084i	−0.274656	−	0.417809i
$29$		−	1.55563i		−	0.288873i	−0.989514	−	0.144436i	$-0.953863\pi$
$29$		−	1.55563i		−	0.288873i	0.989514	−	0.144436i	$-0.0461369\pi$
$30$	−0.637899	−	2.14315i	−0.116464	−	0.391284i
$31$	3.37208	−	1.94687i	0.605643	−	0.349668i	−0.165615	−	0.986190i	$-0.552961\pi$
$31$	3.37208	−	1.94687i	0.605643	−	0.349668i	0.771258	+	0.636522i	$0.219628\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−1.17878	−	4.39926i	−0.205199	−	0.765813i
$34$	−4.12440			−0.707328
$35$	2.01325	+	5.56299i	0.340301	+	0.940317i
$36$	−1.00000			−0.166667
$37$	−2.95980	−	11.0461i	−0.486589	−	1.81597i	−0.572797	−	0.819697i	$-0.694142\pi$
$37$	−2.95980	−	11.0461i	−0.486589	−	1.81597i	0.0862078	−	0.996277i	$-0.472525\pi$
$38$	3.65035	+	0.978107i	0.592164	+	0.158670i
$39$	−2.17725	+	1.25704i	−0.348640	+	0.201287i
$40$	−1.96650	−	1.06437i	−0.310931	−	0.168292i
$41$		−	11.3796i		−	1.77720i	−0.458682	−	0.888600i	$-0.651678\pi$
$41$		−	11.3796i		−	1.77720i	0.458682	−	0.888600i	$-0.348322\pi$
$42$	2.64131	−	0.153213i	0.407563	−	0.0236412i
$43$	0.367260	+	0.367260i	0.0560066	+	0.0560066i	0.734555	−	0.678549i	$-0.237391\pi$
$43$	0.367260	+	0.367260i	0.0560066	+	0.0560066i	−0.678549	+	0.734555i	$0.737391\pi$
$44$	−3.94427	−	2.27722i	−0.594621	−	0.343304i
$45$	2.17497	+	0.519137i	0.324225	+	0.0773884i
$46$	−4.02648	−	6.97408i	−0.593673	−	1.02827i
$47$	4.87829	−	1.30713i	0.711572	−	0.190665i	0.115164	−	0.993347i	$-0.463261\pi$
$47$	4.87829	−	1.30713i	0.711572	−	0.190665i	0.596408	+	0.802681i	$0.296594\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	−6.95305	+	0.809365i	−0.993293	+	0.115624i
$50$	3.72452	+	3.33586i	0.526727	+	0.471762i
$51$	2.06220	−	3.57183i	0.288765	−	0.500156i
$52$	−0.650691	+	2.42841i	−0.0902346	+	0.336760i
$53$	−2.18307	+	8.14732i	−0.299868	+	1.11912i	0.637407	+	0.770528i	$0.280007\pi$
$53$	−2.18307	+	8.14732i	−0.299868	+	1.11912i	−0.937274	+	0.348593i	$0.886659\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	7.39647	+	7.00051i	0.997340	+	0.943949i
$56$	1.75935	−	1.97603i	0.235103	−	0.264058i
$57$	−2.67224	+	2.67224i	−0.353947	+	0.353947i
$58$	1.50262	−	0.402626i	0.197304	−	0.0528674i
$59$	−0.221511	−	0.383668i	−0.0288383	−	0.0499493i	0.851246	−	0.524767i	$-0.175847\pi$
$59$	−0.221511	−	0.383668i	−0.0288383	−	0.0499493i	−0.880084	+	0.474817i	$0.842514\pi$
$60$	1.90502	−	1.17085i	0.245937	−	0.151156i
$61$	7.09442	+	4.09597i	0.908348	+	0.524435i	0.879899	−	0.475160i	$-0.157610\pi$
$61$	7.09442	+	4.09597i	0.908348	+	0.524435i	0.0284488	+	0.999595i	$0.490943\pi$
$62$	2.75329	+	2.75329i	0.349668	+	0.349668i
$63$	−1.18797	+	2.36405i	−0.149670	+	0.297842i
$64$			1.00000i			0.125000i
$65$	2.67591	−	4.94392i	0.331906	−	0.613218i
$66$	3.94427	−	2.27722i	0.485506	−	0.280307i
$67$	−8.99808	−	2.41103i	−1.09929	−	0.294554i	−0.336815	−	0.941571i	$-0.609350\pi$
$67$	−8.99808	−	2.41103i	−1.09929	−	0.294554i	−0.762476	+	0.647017i	$0.776016\pi$
$68$	−1.06747	−	3.98386i	−0.129450	−	0.483114i
$69$	8.05297			0.969464
$70$	−4.85237	+	3.38446i	−0.579969	+	0.404520i
$71$	−6.68403			−0.793248			−0.396624	−	0.917981i	$-0.629818\pi$
$71$	−6.68403			−0.793248			−0.396624	+	0.917981i	$0.629818\pi$
$72$	−0.258819	−	0.965926i	−0.0305021	−	0.113835i
$73$	−4.20080	−	1.12560i	−0.491666	−	0.131742i	0.00446349	−	0.999990i	$-0.498579\pi$
$73$	−4.20080	−	1.12560i	−0.491666	−	0.131742i	−0.496130	+	0.868249i	$0.665246\pi$
$74$	9.90370	−	5.71790i	1.15128	−	0.664693i
$75$	−4.75120	+	1.55760i	−0.548621	+	0.179856i
$76$			3.77912i			0.433494i
$77$	−10.0691	+	6.61917i	−1.14748	+	0.754324i
$78$	−1.77772	−	1.77772i	−0.201287	−	0.201287i
$79$	−4.08283	−	2.35722i	−0.459354	−	0.265208i	0.252418	−	0.967618i	$-0.418774\pi$
$79$	−4.08283	−	2.35722i	−0.459354	−	0.265208i	−0.711773	+	0.702410i	$0.752107\pi$
$80$	0.519137	−	2.17497i	0.0580413	−	0.243169i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	10.9919	−	2.94527i	1.21385	−	0.325250i
$83$	−3.21718	+	3.21718i	−0.353131	+	0.353131i	−0.861273	−	0.508142i	$-0.830332\pi$
$83$	−3.21718	+	3.21718i	−0.353131	+	0.353131i	0.508142	+	0.861273i	$0.330332\pi$
$84$	0.831614	+	2.51166i	0.0907365	+	0.274044i
$85$	0.253550	+	9.21894i	0.0275014	+	0.999935i
$86$	−0.259692	+	0.449799i	−0.0280033	+	0.0485031i
$87$	−0.402626	+	1.50262i	−0.0431660	+	0.161098i
$88$	1.17878	−	4.39926i	0.125658	−	0.468963i
$89$	3.02425	−	5.23816i	0.320570	−	0.555244i	−0.660035	−	0.751234i	$-0.729459\pi$
$89$	3.02425	−	5.23816i	0.320570	−	0.555244i	0.980606	+	0.195990i	$0.0627921\pi$
$90$	0.0614757	+	2.23522i	0.00648011	+	0.235613i
$91$	4.96788	+	4.42314i	0.520775	+	0.463671i
$92$	5.69431	−	5.69431i	0.593673	−	0.593673i
$93$	−3.76106	+	1.00777i	−0.390004	+	0.104501i
$94$	2.52519	+	4.37376i	0.260453	+	0.451118i
$95$	1.96188	−	8.21947i	0.201285	−	0.843299i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	0.462652	+	0.462652i	0.0469752	+	0.0469752i	0.730204	−	0.683229i	$-0.239425\pi$
$97$	0.462652	+	0.462652i	0.0469752	+	0.0469752i	−0.683229	+	0.730204i	$0.739425\pi$
$98$	−2.58137	−	6.50665i	−0.260758	−	0.657271i
$99$			4.55445i			0.457739i
$100$	−2.25822	+	4.46099i	−0.225822	+	0.446099i
$101$	−4.85151	+	2.80102i	−0.482743	+	0.278712i	−0.721559	−	0.692353i	$-0.756574\pi$
$101$	−4.85151	+	2.80102i	−0.482743	+	0.278712i	0.238816	+	0.971065i	$0.423241\pi$
$102$	3.98386	+	1.06747i	0.394461	+	0.105695i
$103$	−1.43852	−	5.36863i	−0.141742	−	0.528987i	−0.999879	−	0.0155666i	$-0.995045\pi$
$103$	−1.43852	−	5.36863i	−0.141742	−	0.528987i	0.858137	−	0.513420i	$-0.171622\pi$
$104$	−2.51408			−0.246525
$105$	−0.504841	−	5.89450i	−0.0492675	−	0.575244i
$106$	−8.43473			−0.819253
$107$	1.93865	+	7.23514i	0.187416	+	0.699447i	0.994100	+	0.108464i	$0.0345932\pi$
$107$	1.93865	+	7.23514i	0.187416	+	0.699447i	−0.806684	+	0.590983i	$0.798740\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	1.27034	−	0.733433i	0.121677	−	0.0702501i	−0.437926	−	0.899011i	$-0.644287\pi$
$109$	1.27034	−	0.733433i	0.121677	−	0.0702501i	0.559603	+	0.828761i	$0.310954\pi$
$110$	−4.84763	+	8.95631i	−0.462203	+	0.853951i
$111$			11.4358i			1.08544i
$112$	2.36405	+	1.18797i	0.223382	+	0.112253i
$113$	7.08834	+	7.08834i	0.666815	+	0.666815i	0.956977	−	0.290163i	$-0.0937094\pi$
$113$	7.08834	+	7.08834i	0.666815	+	0.666815i	−0.290163	+	0.956977i	$0.593709\pi$
$114$	−3.27281	−	1.88956i	−0.306527	−	0.176973i
$115$	−15.3411	+	9.42883i	−1.43056	+	0.879243i
$116$	0.777814	+	1.34721i	0.0722182	+	0.125086i
$117$	2.42841	−	0.650691i	0.224507	−	0.0601564i
$118$	0.313264	−	0.313264i	0.0288383	−	0.0288383i
$119$	−10.6862	−	2.20915i	−0.979599	−	0.202512i
$120$	1.62401	+	1.53707i	0.148251	+	0.140315i
$121$	−4.87150	+	8.43768i	−0.442863	+	0.767062i
$122$	−2.12023	+	7.91280i	−0.191957	+	0.716391i
$123$	−2.94527	+	10.9919i	−0.265566	+	0.991105i
$124$	−1.94687	+	3.37208i	−0.174834	+	0.302821i
$125$	7.22742	−	8.53020i	0.646440	−	0.762965i
$126$	−2.59097	−	0.535629i	−0.230822	−	0.0477177i
$127$	12.9176	−	12.9176i	1.14625	−	1.14625i	0.158971	−	0.987283i	$-0.449182\pi$
$127$	12.9176	−	12.9176i	1.14625	−	1.14625i	0.987283	−	0.158971i	$-0.0508176\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−0.259692	−	0.449799i	−0.0228646	−	0.0396026i
$130$	5.46804	+	1.30515i	0.479579	+	0.114469i
$131$	0.323655	+	0.186862i	0.0282779	+	0.0163262i	0.514072	−	0.857747i	$-0.328136\pi$
$131$	0.323655	+	0.186862i	0.0282779	+	0.0163262i	−0.485794	+	0.874073i	$0.661470\pi$
$132$	3.22048	+	3.22048i	0.280307	+	0.280307i
$133$	8.93402	+	4.48947i	0.774677	+	0.389287i
$134$		−	9.31550i		−	0.804737i
$135$	−1.96650	−	1.06437i	−0.169249	−	0.0916065i
$136$	3.57183	−	2.06220i	0.306282	−	0.176832i
$137$	2.56800	+	0.688094i	0.219399	+	0.0587878i	0.366844	−	0.930282i	$-0.380438\pi$
$137$	2.56800	+	0.688094i	0.219399	+	0.0587878i	−0.147445	+	0.989070i	$0.547105\pi$
$138$	2.08426	+	7.77857i	0.177424	+	0.662156i
$139$	4.58070			0.388530			0.194265	−	0.980949i	$-0.437768\pi$
$139$	4.58070			0.388530			0.194265	+	0.980949i	$0.437768\pi$
$140$	−4.52502	−	3.81106i	−0.382434	−	0.322094i
$141$	−5.05038			−0.425319
$142$	−1.72995	−	6.45627i	−0.145174	−	0.541798i
$143$	11.0601	+	2.96354i	0.924889	+	0.247823i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	−0.992333	−	3.33394i	−0.0824088	−	0.276869i
$146$		−	4.34898i		−	0.359925i
$147$	6.92561	+	1.01780i	0.571215	+	0.0839463i
$148$	8.08634	+	8.08634i	0.664693	+	0.664693i
$149$	14.9338	+	8.62203i	1.22342	+	0.706344i	0.965646	−	0.259860i	$-0.0836764\pi$
$149$	14.9338	+	8.62203i	1.22342	+	0.706344i	0.257778	+	0.966204i	$0.417010\pi$
$150$	−2.73423	−	4.18617i	−0.223249	−	0.341799i
$151$	2.78385	+	4.82177i	0.226546	+	0.392390i	0.956782	−	0.290805i	$-0.0939231\pi$
$151$	2.78385	+	4.82177i	0.226546	+	0.392390i	−0.730236	+	0.683195i	$0.760590\pi$
$152$	−3.65035	+	0.978107i	−0.296082	+	0.0793350i
$153$	−2.91639	+	2.91639i	−0.235776	+	0.235776i
$154$	−8.99971	−	8.01287i	−0.725217	−	0.645696i
$155$	5.98495	−	6.32347i	0.480723	−	0.507914i
$156$	1.25704	−	2.17725i	0.100644	−	0.174320i
$157$	−1.06916	+	3.99014i	−0.0853279	+	0.318448i	−0.995376	−	0.0960544i	$-0.969378\pi$
$157$	−1.06916	+	3.99014i	−0.0853279	+	0.318448i	0.910048	+	0.414503i	$0.136044\pi$
$158$	1.22019	−	4.55381i	0.0970730	−	0.362281i
$159$	4.21737	−	7.30469i	0.334459	−	0.579300i
$160$	2.23522	−	0.0614757i	0.176710	−	0.00486008i
$161$	−6.69696	−	20.2263i	−0.527795	−	1.59406i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	20.9982	−	5.62644i	1.64470	−	0.440697i	0.686580	−	0.727054i	$-0.259111\pi$
$163$	20.9982	−	5.62644i	1.64470	−	0.440697i	0.958123	+	0.286357i	$0.0924445\pi$
$164$	5.68982	+	9.85506i	0.444300	+	0.769551i
$165$	−5.33258	−	8.67632i	−0.415141	−	0.675451i
$166$	−3.94022	−	2.27489i	−0.305821	−	0.176566i
$167$	−17.4949	−	17.4949i	−1.35380	−	1.35380i	−0.881371	−	0.472425i	$-0.843379\pi$
$167$	−17.4949	−	17.4949i	−1.35380	−	1.35380i	−0.472425	−	0.881371i	$-0.656621\pi$
$168$	−2.21084	+	1.45334i	−0.170570	+	0.112128i
$169$			6.67942i			0.513802i
$170$	−8.83919	+	2.63095i	−0.677935	+	0.201785i
$171$	3.27281	−	1.88956i	0.250278	−	0.144498i
$172$	−0.501686	−	0.134426i	−0.0382532	−	0.0102499i
$173$	−4.28763	−	16.0017i	−0.325982	−	1.21658i	−0.913321	−	0.407241i	$-0.866491\pi$
$173$	−4.28763	−	16.0017i	−0.325982	−	1.21658i	0.587338	−	0.809342i	$-0.300176\pi$
$174$	−1.55563			−0.117932
$175$	7.86331	+	10.6381i	0.594411	+	0.804162i
$176$	4.55445			0.343304
$177$	0.114663	+	0.427926i	0.00861856	+	0.0321649i
$178$	5.84241	+	1.56547i	0.437907	+	0.117337i
$179$	−11.0222	+	6.36367i	−0.823837	+	0.475643i	−0.851738	−	0.523968i	$-0.824451\pi$
$179$	−11.0222	+	6.36367i	−0.823837	+	0.475643i	0.0279007	+	0.999611i	$0.491118\pi$
$180$	−2.14315	+	0.637899i	−0.159741	+	0.0475462i
$181$			9.09951i			0.676361i	0.941081	+	0.338180i	$0.109811\pi$
$181$			9.09951i			0.676361i	−0.941081	+	0.338180i	$0.890189\pi$
$182$	−2.98665	+	5.94340i	−0.221385	+	0.440554i
$183$	−5.79257	−	5.79257i	−0.428199	−	0.428199i
$184$	6.97408	+	4.02648i	0.514136	+	0.296836i
$185$	−13.3896	−	21.7855i	−0.984425	−	1.60170i
$186$	−1.94687	−	3.37208i	−0.142751	−	0.247253i
$187$	−18.1443	+	4.86175i	−1.32684	+	0.355526i
$188$	−3.57116	+	3.57116i	−0.260453	+	0.260453i
$189$	1.75935	−	1.97603i	0.127974	−	0.143735i
$190$	8.44717	−	0.232324i	0.612822	−	0.0168545i
$191$	−9.10308	+	15.7670i	−0.658676	+	1.14086i	0.322283	+	0.946643i	$0.395550\pi$
$191$	−9.10308	+	15.7670i	−0.658676	+	1.14086i	−0.980959	+	0.194216i	$0.937784\pi$
$192$	0.258819	−	0.965926i	0.0186787	−	0.0697097i
$193$	−2.60664	+	9.72810i	−0.187630	+	0.700244i	0.806422	+	0.591340i	$0.201401\pi$
$193$	−2.60664	+	9.72810i	−0.187630	+	0.700244i	−0.994052	+	0.108904i	$0.965266\pi$
$194$	−0.327144	+	0.566631i	−0.0234876	+	0.0406817i
$195$	−3.86431	+	4.08289i	−0.276729	+	0.292382i
$196$	5.61684	−	4.17746i	0.401203	−	0.298390i
$197$	16.2439	−	16.2439i	1.15733	−	1.15733i	0.172283	−	0.985048i	$-0.444886\pi$
$197$	16.2439	−	16.2439i	1.15733	−	1.15733i	0.985048	−	0.172283i	$-0.0551142\pi$
$198$	−4.39926	+	1.17878i	−0.312642	+	0.0837721i
$199$	−12.6984	−	21.9943i	−0.900168	−	1.55914i	−0.827275	−	0.561797i	$-0.810110\pi$
$199$	−12.6984	−	21.9943i	−0.900168	−	1.55914i	−0.0728933	−	0.997340i	$-0.523223\pi$
$200$	−4.89346	−	1.02668i	−0.346020	−	0.0725972i
$201$	8.06746	+	4.65775i	0.569035	+	0.328532i
$202$	−3.96124	−	3.96124i	−0.278712	−	0.278712i
$203$	4.10890	−	0.238342i	0.288388	−	0.0167283i
$204$			4.12440i			0.288765i
$205$	−7.25906	−	24.3883i	−0.506995	−	1.70335i
$206$	4.81338	−	2.77901i	0.335364	−	0.193623i
$207$	−7.77857	−	2.08426i	−0.540648	−	0.144866i
$208$	−0.650691	−	2.42841i	−0.0451173	−	0.168380i
$209$	17.2118			1.19056
$210$	5.56299	−	2.01325i	0.383883	−	0.138927i
$211$	−13.6182			−0.937517			−0.468759	−	0.883326i	$-0.655299\pi$
$211$	−13.6182			−0.937517			−0.468759	+	0.883326i	$0.655299\pi$
$212$	−2.18307	−	8.14732i	−0.149934	−	0.559560i
$213$	6.45627	+	1.72995i	0.442377	+	0.118534i
$214$	−6.48684	+	3.74518i	−0.443432	+	0.256015i
$215$	1.02137	+	0.552817i	0.0696566	+	0.0377018i
$216$			1.00000i			0.0680414i
$217$	5.65893	+	8.60842i	0.384153	+	0.584378i
$218$	1.03723	+	1.03723i	0.0702501	+	0.0702501i
$219$	3.76633	+	2.17449i	0.254505	+	0.146939i
$220$	−9.90579	−	2.36438i	−0.667848	−	0.159407i
$221$	5.18452	+	8.97985i	0.348749	+	0.604050i
$222$	−11.0461	+	2.95980i	−0.741369	+	0.198649i
$223$	15.8412	−	15.8412i	1.06081	−	1.06081i	0.0627803	−	0.998027i	$-0.480003\pi$
$223$	15.8412	−	15.8412i	1.06081	−	1.06081i	0.998027	−	0.0627803i	$-0.0199968\pi$
$224$	−0.535629	+	2.59097i	−0.0357883	+	0.173116i
$225$	4.99244	−	0.274824i	0.332829	−	0.0183216i
$226$	−5.01221	+	8.68141i	−0.333407	+	0.577479i
$227$	−2.83476	+	10.5795i	−0.188150	+	0.702184i	0.805785	+	0.592209i	$0.201744\pi$
$227$	−2.83476	+	10.5795i	−0.188150	+	0.702184i	−0.993934	+	0.109976i	$0.964923\pi$
$228$	0.978107	−	3.65035i	0.0647767	−	0.241750i
$229$	−14.4722	+	25.0665i	−0.956347	+	1.65644i	−0.225092	+	0.974338i	$0.572268\pi$
$229$	−14.4722	+	25.0665i	−0.956347	+	1.65644i	−0.731255	+	0.682104i	$0.761065\pi$
$230$	−13.0781	−	12.3780i	−0.862345	−	0.816180i
$231$	11.4392	−	3.78754i	0.752645	−	0.249202i
$232$	−1.09999	+	1.09999i	−0.0722182	+	0.0722182i
$233$	−1.36397	+	0.365476i	−0.0893569	+	0.0239431i	−0.303220	−	0.952920i	$-0.598062\pi$
$233$	−1.36397	+	0.365476i	−0.0893569	+	0.0239431i	0.213864	+	0.976864i	$0.431395\pi$
$234$	1.25704	+	2.17725i	0.0821751	+	0.142332i
$235$	9.62108	−	5.91324i	0.627610	−	0.385737i
$236$	0.383668	+	0.221511i	0.0249747	+	0.0144191i
$237$	3.33362	+	3.33362i	0.216542	+	0.216542i
$238$	−0.631910	−	10.8938i	−0.0409606	−	0.706141i
$239$		−	4.36430i		−	0.282303i	−0.989988	−	0.141152i	$-0.954920\pi$
$239$		−	4.36430i		−	0.282303i	0.989988	−	0.141152i	$-0.0450805\pi$
$240$	−1.06437	+	1.96650i	−0.0687049	+	0.126937i
$241$	−2.65862	+	1.53496i	−0.171257	+	0.0988752i	−0.583178	−	0.812344i	$-0.698191\pi$
$241$	−2.65862	+	1.53496i	−0.171257	+	0.0988752i	0.411922	+	0.911219i	$0.364858\pi$
$242$	−9.41101	−	2.52167i	−0.604963	−	0.162099i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	−8.19194			−0.524435
$245$	−14.3851	+	6.16994i	−0.919032	+	0.394183i
$246$	−11.3796			−0.725539
$247$	−2.45904	−	9.17725i	−0.156465	−	0.583934i
$248$	−3.76106	−	1.00777i	−0.238828	−	0.0639937i
$249$	3.94022	−	2.27489i	0.249701	−	0.144165i
$250$	10.1101	+	4.77337i	0.639421	+	0.301895i
$251$		−	1.25355i		−	0.0791234i	−0.999217	−	0.0395617i	$-0.987404\pi$
$251$		−	1.25355i		−	0.0791234i	0.999217	−	0.0395617i	$-0.0125962\pi$
$252$	−0.153213	−	2.64131i	−0.00965150	−	0.166387i
$253$	−25.9344	−	25.9344i	−1.63048	−	1.63048i
$254$	15.8208	+	9.13414i	0.992685	+	0.573127i
$255$	2.14113	−	8.97044i	0.134083	−	0.561751i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.81783	−	1.82683i	0.425285	−	0.113955i	−0.0398273	−	0.999207i	$-0.512681\pi$
$257$	6.81783	−	1.82683i	0.425285	−	0.113955i	0.465112	+	0.885252i	$0.346014\pi$
$258$	0.367260	−	0.367260i	0.0228646	−	0.0228646i
$259$	28.7228	−	9.51018i	1.78475	−	0.590934i
$260$	0.154555	+	5.61952i	0.00958507	+	0.348508i
$261$	0.777814	−	1.34721i	0.0481455	−	0.0833904i
$262$	−0.0967271	+	0.360990i	−0.00597582	+	0.0223021i
$263$	−1.47214	+	5.49409i	−0.0907758	+	0.338780i	−0.996345	−	0.0854182i	$-0.972777\pi$
$263$	−1.47214	+	5.49409i	−0.0907758	+	0.338780i	0.905569	+	0.424198i	$0.139444\pi$
$264$	−2.27722	+	3.94427i	−0.140153	+	0.242753i
$265$	0.518531	+	18.8535i	0.0318531	+	1.15816i
$266$	−2.02421	+	9.79156i	−0.124112	+	0.600359i
$267$	−4.27694	+	4.27694i	−0.261745	+	0.261745i
$268$	8.99808	−	2.41103i	0.549645	−	0.147277i
$269$	3.85391	+	6.67517i	0.234977	+	0.406992i	0.959266	−	0.282504i	$-0.0911652\pi$
$269$	3.85391	+	6.67517i	0.234977	+	0.406992i	−0.724289	+	0.689496i	$0.757832\pi$
$270$	0.519137	−	2.17497i	0.0315937	−	0.132364i
$271$	−15.4900	−	8.94316i	−0.940951	−	0.543258i	−0.0506925	−	0.998714i	$-0.516143\pi$
$271$	−15.4900	−	8.94316i	−0.940951	−	0.543258i	−0.890258	+	0.455456i	$0.849476\pi$
$272$	2.91639	+	2.91639i	0.176832	+	0.176832i
$273$	−3.65381	−	5.55821i	−0.221139	−	0.336398i
$274$			2.65859i			0.160611i
$275$	20.3174	+	10.2849i	1.22518	+	0.620205i
$276$	−6.97408	+	4.02648i	−0.419790	+	0.242366i
$277$	−14.2439	−	3.81664i	−0.855832	−	0.229319i	−0.195881	−	0.980628i	$-0.562756\pi$
$277$	−14.2439	−	3.81664i	−0.855832	−	0.229319i	−0.659951	+	0.751308i	$0.729423\pi$
$278$	1.18557	+	4.42461i	0.0711059	+	0.265371i
$279$	3.89374			0.233112
$280$	2.51004	−	5.35721i	0.150004	−	0.320154i
$281$	0.587402			0.0350415			0.0175207	−	0.999847i	$-0.494423\pi$
$281$	0.587402			0.0350415			0.0175207	+	0.999847i	$0.494423\pi$
$282$	−1.30713	−	4.87829i	−0.0778387	−	0.290498i
$283$	17.9809	+	4.81795i	1.06885	+	0.286398i	0.750021	−	0.661414i	$-0.230043\pi$
$283$	17.9809	+	4.81795i	1.06885	+	0.286398i	0.318830	+	0.947812i	$0.396710\pi$
$284$	5.78854	−	3.34201i	0.343486	−	0.198312i
$285$	−4.02238	+	7.43162i	−0.238266	+	0.440211i
$286$			11.4502i			0.677066i
$287$	30.0572	−	1.74351i	1.77422	−	0.102916i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	−0.00921092	−	0.00531793i	−0.000541819	−	0.000312819i
$290$	2.96350	−	1.82141i	0.174023	−	0.106957i
$291$	−0.327144	−	0.566631i	−0.0191775	−	0.0332165i
$292$	4.20080	−	1.12560i	0.245833	−	0.0658708i
$293$	−20.6736	+	20.6736i	−1.20777	+	1.20777i	−0.236018	+	0.971749i	$0.575842\pi$
$293$	−20.6736	+	20.6736i	−1.20777	+	1.20777i	−0.971749	+	0.236018i	$0.924158\pi$
$294$	0.809365	+	6.95305i	0.0472031	+	0.405510i
$295$	−0.719472	−	0.680956i	−0.0418893	−	0.0396468i
$296$	−5.71790	+	9.90370i	−0.332346	+	0.575641i
$297$	1.17878	−	4.39926i	0.0683996	−	0.255271i
$298$	−4.46309	+	16.6565i	−0.258540	+	0.964884i
$299$	−10.1229	+	17.5334i	−0.585422	+	1.01398i
$300$	3.33586	−	3.72452i	0.192596	−	0.215035i
$301$	−0.913778	+	1.02632i	−0.0526693	+	0.0591559i
$302$	−3.93696	+	3.93696i	−0.226546	+	0.226546i
$303$	5.41115	−	1.44991i	0.310863	−	0.0832954i
$304$	−1.88956	−	3.27281i	−0.108374	−	0.187709i
$305$	17.8172	+	4.25274i	1.02021	+	0.243511i
$306$	−3.57183	−	2.06220i	−0.204188	−	0.117888i
$307$	−1.63464	−	1.63464i	−0.0932937	−	0.0932937i	0.658920	−	0.752213i	$-0.271014\pi$
$307$	−1.63464	−	1.63464i	−0.0932937	−	0.0932937i	−0.752213	+	0.658920i	$0.771014\pi$
$308$	5.41055	−	10.7669i	0.308294	−	0.613503i
$309$			5.55802i			0.316185i
$310$	7.65703	+	4.14439i	0.434890	+	0.235385i
$311$	12.0239	−	6.94197i	0.681810	−	0.393643i	−0.118727	−	0.992927i	$-0.537881\pi$
$311$	12.0239	−	6.94197i	0.681810	−	0.393643i	0.800537	+	0.599284i	$0.204548\pi$
$312$	2.42841	+	0.650691i	0.137482	+	0.0368381i
$313$	3.49157	+	13.0307i	0.197355	+	0.736540i	0.991645	+	0.129000i	$0.0411768\pi$
$313$	3.49157	+	13.0307i	0.197355	+	0.736540i	−0.794289	+	0.607540i	$0.792157\pi$
$314$	−4.13090			−0.233120
$315$	−1.03797	+	5.82431i	−0.0584830	+	0.328163i
$316$	4.71445			0.265208
$317$	3.55024	+	13.2497i	0.199401	+	0.744175i	0.991083	+	0.133242i	$0.0425389\pi$
$317$	3.55024	+	13.2497i	0.199401	+	0.744175i	−0.791682	+	0.610933i	$0.790794\pi$
$318$	8.14732	+	2.18307i	0.456879	+	0.122420i
$319$	6.13581	−	3.54251i	0.343539	−	0.198343i
$320$	0.637899	+	2.14315i	0.0356596	+	0.119806i
$321$		−	7.49036i		−	0.418071i
$322$	17.8038	−	11.7037i	0.992167	−	0.652223i
$323$	11.0214	+	11.0214i	0.613245	+	0.613245i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	2.58115	−	12.3025i	0.143176	−	0.682421i
$326$	10.8694	+	18.8264i	0.602003	+	1.04270i
$327$	−1.41688	+	0.379653i	−0.0783538	+	0.0209948i
$328$	−8.04662	+	8.04662i	−0.444300	+	0.444300i
$329$	4.19996	+	12.6848i	0.231552	+	0.699336i
$330$	7.00051	−	7.39647i	0.385365	−	0.407162i
$331$	−16.6194	+	28.7856i	−0.913483	+	1.58220i	−0.104375	+	0.994538i	$0.533284\pi$
$331$	−16.6194	+	28.7856i	−0.913483	+	1.58220i	−0.809108	+	0.587660i	$0.800049\pi$
$332$	1.17757	−	4.39475i	0.0646275	−	0.241193i
$333$	2.95980	−	11.0461i	0.162196	−	0.605325i
$334$	12.3708	−	21.4268i	0.676898	−	1.17242i
$335$	−20.8222	+	0.572677i	−1.13764	+	0.0312887i
$336$	−1.97603	−	1.75935i	−0.107801	−	0.0959805i
$337$	−17.0329	+	17.0329i	−0.927842	+	0.927842i	−0.997566	−	0.0697246i	$-0.977788\pi$
$337$	−17.0329	+	17.0329i	−0.927842	+	0.927842i	0.0697246	+	0.997566i	$0.477788\pi$
$338$	−6.45183	+	1.72876i	−0.350933	+	0.0940323i
$339$	−5.01221	−	8.68141i	−0.272226	−	0.471509i
$340$	−4.82905	−	7.85706i	−0.261892	−	0.426109i
$341$	15.3579	+	8.86691i	0.831679	+	0.480170i
$342$	2.67224	+	2.67224i	0.144498	+	0.144498i
$343$	−3.20308	−	18.2412i	−0.172950	−	0.984931i
$344$		−	0.519384i		−	0.0280033i
$345$	17.2587	−	5.13698i	0.929178	−	0.276566i
$346$	14.3467	−	8.28306i	0.771283	−	0.445300i
$347$	−1.98700	−	0.532414i	−0.106668	−	0.0285815i	0.205090	−	0.978743i	$-0.434251\pi$
$347$	−1.98700	−	0.532414i	−0.106668	−	0.0285815i	−0.311758	+	0.950162i	$0.600918\pi$
$348$	−0.402626	−	1.50262i	−0.0215830	−	0.0805489i
$349$	−11.7250			−0.627627			−0.313814	−	0.949485i	$-0.601607\pi$
$349$	−11.7250			−0.627627			−0.313814	+	0.949485i	$0.601607\pi$
$350$	−8.24040	+	10.3487i	−0.440468	+	0.553162i
$351$	−2.51408			−0.134191
$352$	1.17878	+	4.39926i	0.0628291	+	0.234481i
$353$	−11.0334	−	2.95640i	−0.587250	−	0.157353i	−0.0470542	−	0.998892i	$-0.514983\pi$
$353$	−11.0334	−	2.95640i	−0.587250	−	0.157353i	−0.540196	+	0.841539i	$0.681650\pi$
$354$	−0.383668	+	0.221511i	−0.0203917	+	0.0117732i
$355$	−14.3249	+	4.26373i	−0.760285	+	0.226296i
$356$			6.04851i			0.320570i
$357$	9.75027	+	4.89966i	0.516039	+	0.259317i
$358$	−8.99958	−	8.99958i	−0.475643	−	0.475643i
$359$	2.08846	+	1.20577i	0.110225	+	0.0636383i	0.554099	−	0.832451i	$-0.313063\pi$
$359$	2.08846	+	1.20577i	0.110225	+	0.0636383i	−0.443874	+	0.896089i	$0.646396\pi$
$360$	−1.17085	−	1.90502i	−0.0617093	−	0.100403i
$361$	2.35914	+	4.08615i	0.124165	+	0.215061i
$362$	−8.78945	+	2.35513i	−0.461963	+	0.123783i
$363$	6.88934	−	6.88934i	0.361596	−	0.361596i
$364$	−6.51388	−	1.34661i	−0.341420	−	0.0705817i
$365$	−9.72095	+	0.267357i	−0.508818	+	0.0139941i
$366$	4.09597	−	7.09442i	0.214100	−	0.370832i
$367$	1.34815	−	5.03135i	0.0703727	−	0.262635i	−0.921772	−	0.387733i	$-0.873258\pi$
$367$	1.34815	−	5.03135i	0.0703727	−	0.262635i	0.992144	+	0.125099i	$0.0399248\pi$
$368$	−2.08426	+	7.77857i	−0.108650	+	0.405486i
$369$	5.68982	−	9.85506i	0.296200	−	0.513034i
$370$	17.5777	−	18.5719i	0.913819	−	0.965506i
$371$	−21.8541	−	4.51789i	−1.13461	−	0.234557i
$372$	2.75329	−	2.75329i	0.142751	−	0.142751i
$373$	0.141659	−	0.0379573i	0.00733480	−	0.00196535i	−0.255150	−	0.966902i	$-0.582125\pi$
$373$	0.141659	−	0.0379573i	0.00733480	−	0.00196535i	0.262485	+	0.964936i	$0.415458\pi$
$374$	−9.39217	−	16.2677i	−0.485658	−	0.841184i
$375$	−9.18893	+	6.36895i	−0.474514	+	0.328891i
$376$	−4.37376	−	2.52519i	−0.225559	−	0.130227i
$377$	−2.76547	−	2.76547i	−0.142429	−	0.142429i
$378$	2.36405	+	1.18797i	0.121594	+	0.0611026i
$379$			18.5438i			0.952530i	0.879302	+	0.476265i	$0.158010\pi$
$379$			18.5438i			0.952530i	−0.879302	+	0.476265i	$0.841990\pi$
$380$	2.41069	+	8.09921i	0.123666	+	0.415481i
$381$	−15.8208	+	9.13414i	−0.810524	+	0.467956i
$382$	−17.5858	−	4.71210i	−0.899768	−	0.241092i
$383$	−0.996351	−	3.71843i	−0.0509112	−	0.190003i	0.935787	−	0.352566i	$-0.114691\pi$
$383$	−0.996351	−	3.71843i	−0.0509112	−	0.190003i	−0.986698	+	0.162563i	$0.948024\pi$
$384$	1.00000			0.0510310
$385$	−17.3573	+	20.6090i	−0.884610	+	1.05033i
$386$	−10.0713			−0.512614
$387$	0.134426	+	0.501686i	0.00683328	+	0.0255021i
$388$	−0.631994	−	0.169342i	−0.0320847	−	0.00859706i
$389$	−15.4340	+	8.91085i	−0.782537	+	0.451798i	−0.837329	−	0.546700i	$-0.815884\pi$
$389$	−15.4340	+	8.91085i	−0.782537	+	0.451798i	0.0547917	+	0.998498i	$0.482551\pi$
$390$	−4.94392	−	2.67591i	−0.250345	−	0.135500i
$391$		−	33.2136i		−	1.67969i
$392$	5.48886	+	4.34424i	0.277229	+	0.219417i
$393$	−0.264263	−	0.264263i	−0.0133303	−	0.0133303i
$394$	19.8946	+	11.4862i	1.00228	+	0.578665i
$395$	−10.2538	−	2.44745i	−0.515924	−	0.123144i
$396$	−2.27722	−	3.94427i	−0.114435	−	0.198207i
$397$	24.7725	−	6.63778i	1.24330	−	0.333141i	0.423554	−	0.905871i	$-0.360782\pi$
$397$	24.7725	−	6.63778i	1.24330	−	0.333141i	0.819744	+	0.572730i	$0.194116\pi$
$398$	17.9583	−	17.9583i	0.900168	−	0.900168i
$399$	−7.46764	−	6.64879i	−0.373849	−	0.332856i
$400$	−0.274824	−	4.99244i	−0.0137412	−	0.249622i
$401$	2.63060	−	4.55632i	0.131366	−	0.227532i	−0.792838	−	0.609433i	$-0.791397\pi$
$401$	2.63060	−	4.55632i	0.131366	−	0.227532i	0.924203	+	0.381901i	$0.124730\pi$
$402$	−2.41103	+	8.99808i	−0.120251	+	0.448784i
$403$	2.53362	−	9.45560i	0.126209	−	0.471017i
$404$	2.80102	−	4.85151i	0.139356	−	0.241371i
$405$	1.62401	+	1.53707i	0.0806978	+	0.0763777i
$406$	1.29368	+	3.90720i	0.0642043	+	0.193911i
$407$	36.8288	−	36.8288i	1.82554	−	1.82554i
$408$	−3.98386	+	1.06747i	−0.197230	+	0.0528477i
$409$	−4.18773	−	7.25336i	−0.207070	−	0.358655i	0.743720	−	0.668491i	$-0.233059\pi$
$409$	−4.18773	−	7.25336i	−0.207070	−	0.358655i	−0.950790	+	0.309835i	$0.899726\pi$
$410$	21.6785	−	13.3239i	1.07062	−	0.658018i
$411$	−2.30241	−	1.32929i	−0.113569	−	0.0655693i
$412$	3.93011	+	3.93011i	0.193623	+	0.193623i
$413$	0.979449	−	0.643862i	0.0481955	−	0.0316824i
$414$		−	8.05297i		−	0.395782i
$415$	−4.84265	+	8.94712i	−0.237717	+	0.439197i
$416$	2.17725	−	1.25704i	0.106749	−	0.0616313i
$417$	−4.42461	−	1.18557i	−0.216674	−	0.0580577i
$418$	4.45474	+	16.6253i	0.217888	+	0.813170i
$419$	−9.53078			−0.465609			−0.232805	−	0.972524i	$-0.574790\pi$
$419$	−9.53078			−0.465609			−0.232805	+	0.972524i	$0.574790\pi$
$420$	3.38446	+	4.85237i	0.165145	+	0.236771i
$421$	16.8461			0.821027			0.410514	−	0.911854i	$-0.365349\pi$
$421$	16.8461			0.821027			0.410514	+	0.911854i	$0.365349\pi$
$422$	−3.52466	−	13.1542i	−0.171578	−	0.640336i
$423$	4.87829	+	1.30713i	0.237191	+	0.0635550i
$424$	7.30469	−	4.21737i	0.354747	−	0.204813i
$425$	6.42415	+	19.5958i	0.311617	+	0.950537i
$426$			6.68403i			0.323842i
$427$	−9.73177	+	19.3661i	−0.470953	+	0.937193i
$428$	−5.29649	−	5.29649i	−0.256015	−	0.256015i
$429$	−9.91619	−	5.72511i	−0.478758	−	0.276411i
$430$	−0.269631	+	1.12964i	−0.0130028	+	0.0544763i
$431$	−10.7791	−	18.6699i	−0.519209	−	0.899297i	−0.999751	−	0.0223251i	$-0.992893\pi$
$431$	−10.7791	−	18.6699i	−0.519209	−	0.899297i	0.480541	−	0.876972i	$-0.340440\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	−25.8823	+	25.8823i	−1.24382	+	1.24382i	−0.285422	+	0.958402i	$0.592134\pi$
$433$	−25.8823	+	25.8823i	−1.24382	+	1.24382i	−0.958402	+	0.285422i	$0.907866\pi$
$434$	−6.85045	+	7.69413i	−0.328832	+	0.369330i
$435$	0.0956333	+	3.47717i	0.00458526	+	0.166718i
$436$	−0.733433	+	1.27034i	−0.0351251	+	0.0608384i
$437$	−7.87667	+	29.3961i	−0.376792	+	1.40621i
$438$	−1.12560	+	4.20080i	−0.0537832	+	0.200722i
$439$	−10.5899	+	18.3422i	−0.505426	+	0.875424i	0.494554	+	0.869147i	$0.335331\pi$
$439$	−10.5899	+	18.3422i	−0.505426	+	0.875424i	−0.999980	+	0.00627716i	$0.998002\pi$
$440$	−0.279988	−	10.1802i	−0.0133479	−	0.485322i
$441$	−6.42620	−	2.77559i	−0.306010	−	0.132171i
$442$	−7.33202	+	7.33202i	−0.348749	+	0.348749i
$443$	4.00895	−	1.07420i	0.190471	−	0.0510366i	−0.162322	−	0.986738i	$-0.551898\pi$
$443$	4.00895	−	1.07420i	0.190471	−	0.0510366i	0.352794	+	0.935701i	$0.385232\pi$
$444$	−5.71790	−	9.90370i	−0.271360	−	0.470009i
$445$	3.14001	−	13.1553i	0.148851	−	0.623622i
$446$	19.4015	+	11.2014i	0.918686	+	0.530404i
$447$	−12.1934	−	12.1934i	−0.576728	−	0.576728i
$448$	−2.64131	+	0.153213i	−0.124790	+	0.00723862i
$449$			29.3795i			1.38651i	0.720694	+	0.693253i	$0.243823\pi$
$449$			29.3795i			1.38651i	−0.720694	+	0.693253i	$0.756177\pi$
$450$	1.55760	+	4.75120i	0.0734259	+	0.223974i
$451$	44.8843	−	25.9140i	2.11352	−	1.22024i
$452$	−9.68285	−	2.59451i	−0.455443	−	0.122036i
$453$	−1.44103	−	5.37799i	−0.0677053	−	0.252680i
$454$	−10.9527			−0.514035
$455$	13.4684	+	6.31044i	0.631410	+	0.295838i
$456$	3.77912			0.176973
$457$	−0.121995	−	0.455291i	−0.00570668	−	0.0212976i	0.963014	−	0.269452i	$-0.0868426\pi$
$457$	−0.121995	−	0.455291i	−0.00570668	−	0.0212976i	−0.968720	+	0.248155i	$0.920176\pi$
$458$	−27.9581	−	7.49134i	−1.30639	−	0.350047i
$459$	3.57183	−	2.06220i	0.166719	−	0.0962551i
$460$	8.57135	−	15.8361i	0.399641	−	0.738364i
$461$		−	26.3199i		−	1.22584i	−0.790145	−	0.612920i	$-0.789995\pi$
$461$		−	26.3199i		−	1.22584i	0.790145	−	0.612920i	$-0.210005\pi$
$462$	6.61917	+	10.0691i	0.307952	+	0.468459i
$463$	−1.02619	−	1.02619i	−0.0476909	−	0.0476909i	0.682859	−	0.730550i	$-0.260736\pi$
$463$	−1.02619	−	1.02619i	−0.0476909	−	0.0476909i	−0.730550	+	0.682859i	$0.760736\pi$
$464$	−1.34721	−	0.777814i	−0.0625428	−	0.0361091i
$465$	−7.41766	+	4.55899i	−0.343986	+	0.211418i
$466$	−0.706045	−	1.22291i	−0.0327069	−	0.0566500i
$467$	−29.9569	+	8.02693i	−1.38624	+	0.371442i	−0.873384	−	0.487033i	$-0.838079\pi$
$467$	−29.9569	+	8.02693i	−1.38624	+	0.371442i	−0.512856	+	0.858475i	$0.671413\pi$
$468$	−1.77772	+	1.77772i	−0.0821751	+	0.0821751i
$469$	4.98966	−	24.1361i	0.230401	−	1.11450i
$470$	8.20187	+	7.76279i	0.378324	+	0.358071i
$471$	2.06545	−	3.57747i	0.0951709	−	0.164841i
$472$	−0.114663	+	0.427926i	−0.00527777	+	0.0196969i
$473$	−0.612238	+	2.28490i	−0.0281507	+	0.105060i
$474$	−2.35722	+	4.08283i	−0.108271	+	0.187531i
$475$	−1.03859	−	18.8670i	−0.0476538	−	0.865678i
$476$	10.3591	−	3.42990i	0.474807	−	0.157209i
$477$	−5.96425	+	5.96425i	−0.273084	+	0.273084i
$478$	4.21559	−	1.12956i	0.192817	−	0.0516650i
$479$	−16.6760	−	28.8837i	−0.761945	−	1.31973i	−0.941847	−	0.336043i	$-0.890911\pi$
$479$	−16.6760	−	28.8837i	−0.761945	−	1.31973i	0.179901	−	0.983685i	$-0.442422\pi$
$480$	−2.17497	−	0.519137i	−0.0992734	−	0.0236953i
$481$	−24.8987	−	14.3752i	−1.13528	−	0.655455i
$482$	−2.17075	−	2.17075i	−0.0988752	−	0.0988752i
$483$	1.23382	+	21.2704i	0.0561407	+	0.967837i
$484$		−	9.74299i		−	0.442863i
$485$	1.28666	+	0.696407i	0.0584241	+	0.0316222i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	3.19111	+	0.855056i	0.144603	+	0.0387463i	0.330395	−	0.943843i	$-0.392818\pi$
$487$	3.19111	+	0.855056i	0.144603	+	0.0387463i	−0.185791	+	0.982589i	$0.559485\pi$
$488$	−2.12023	−	7.91280i	−0.0959783	−	0.358196i
$489$	−21.7389			−0.983067
$490$	−9.68285	−	12.2981i	−0.437426	−	0.555570i
$491$	3.61649			0.163210			0.0816051	−	0.996665i	$-0.473995\pi$
$491$	3.61649			0.163210			0.0816051	+	0.996665i	$0.473995\pi$
$492$	−2.94527	−	10.9919i	−0.132783	−	0.495552i
$493$	6.19740	+	1.66059i	0.279117	+	0.0747891i
$494$	8.22809	−	4.75049i	0.370199	−	0.213735i
$495$	2.90528	+	9.76086i	0.130583	+	0.438718i
$496$		−	3.89374i		−	0.174834i
$497$	−1.02408	−	17.6546i	−0.0459362	−	0.791917i
$498$	3.21718	+	3.21718i	0.144165	+	0.144165i
$499$	0.561004	+	0.323896i	0.0251140	+	0.0144996i	0.512504	−	0.858685i	$-0.328718\pi$
$499$	0.561004	+	0.323896i	0.0251140	+	0.0144996i	−0.487390	+	0.873184i	$0.662051\pi$
$500$	−1.99403	+	11.0011i	−0.0891757	+	0.491983i
$501$	12.3708	+	21.4268i	0.552685	+	0.957278i
$502$	1.21084	−	0.324443i	0.0540423	−	0.0144806i
$503$	12.9189	−	12.9189i	0.576027	−	0.576027i	−0.357779	−	0.933806i	$-0.616466\pi$
$503$	12.9189	−	12.9189i	0.576027	−	0.576027i	0.933806	+	0.357779i	$0.116466\pi$
$504$	2.51166	−	0.831614i	0.111878	−	0.0370430i
$505$	−8.61073	+	9.09777i	−0.383172	+	0.404845i
$506$	18.3384	−	31.7631i	0.815242	−	1.41204i
$507$	1.72876	−	6.45183i	0.0767770	−	0.286536i
$508$	−4.72818	+	17.6458i	−0.209779	+	0.782906i
$509$	10.1554	−	17.5896i	0.450128	−	0.779645i	−0.548265	−	0.836304i	$-0.684712\pi$
$509$	10.1554	−	17.5896i	0.450128	−	0.779645i	0.998394	+	0.0566595i	$0.0180449\pi$
$510$	9.21894	−	0.253550i	0.408222	−	0.0112274i
$511$	2.32944	−	11.2681i	0.103049	−	0.498470i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.65035	+	0.978107i	−0.161167	+	0.0431845i
$514$	3.52917	+	6.11270i	0.155665	+	0.269620i
$515$	−6.50761	−	10.5881i	−0.286760	−	0.466569i
$516$	0.449799	+	0.259692i	0.0198013	+	0.0114323i
$517$	16.2646	+	16.2646i	0.715318	+	0.715318i
$518$	16.6201	+	25.2827i	0.730247	+	1.11086i
$519$			16.5661i			0.727172i
$520$	−5.38804	+	1.60373i	−0.236281	+	0.0703281i
$521$	1.07875	−	0.622814i	0.0472607	−	0.0272860i	−0.476183	−	0.879346i	$-0.657980\pi$
$521$	1.07875	−	0.622814i	0.0472607	−	0.0272860i	0.523444	+	0.852060i	$0.324647\pi$
$522$	1.50262	+	0.402626i	0.0657679	+	0.0176225i
$523$	5.25224	+	19.6016i	0.229664	+	0.857119i	0.980482	+	0.196609i	$0.0629930\pi$
$523$	5.25224	+	19.6016i	0.229664	+	0.857119i	−0.750818	+	0.660509i	$0.770340\pi$
$524$	−0.373725			−0.0163262
$525$	−4.84205	−	12.3108i	−0.211324	−	0.537285i
$526$	−5.68790			−0.248004
$527$	4.15646	+	15.5121i	0.181058	+	0.675718i
$528$	−4.39926	−	1.17878i	−0.191453	−	0.0512997i
$529$	36.2434	−	20.9252i	1.57580	−	0.909790i
$530$	−18.0769	+	5.38051i	−0.785209	+	0.233714i
$531$		−	0.443022i		−	0.0192255i
$532$	−9.98182	+	0.579009i	−0.432767	+	0.0251032i
$533$	−20.2298	−	20.2298i	−0.876250	−	0.876250i
$534$	−5.23816	−	3.02425i	−0.226677	−	0.130872i
$535$	8.77010	+	14.2693i	0.379164	+	0.616916i
$536$	4.65775	+	8.06746i	0.201184	+	0.348461i
$537$	12.2937	−	3.29408i	0.530510	−	0.142150i
$538$	−5.45025	+	5.45025i	−0.234977	+	0.234977i
$539$	−19.0260	−	25.5816i	−0.819508	−	1.10188i
$540$	2.23522	−	0.0614757i	0.0961887	−	0.00264549i
$541$	17.0068	−	29.4566i	0.731178	−	1.26644i	−0.225202	−	0.974312i	$-0.572304\pi$
$541$	17.0068	−	29.4566i	0.731178	−	1.26644i	0.956380	−	0.292126i	$-0.0943625\pi$
$542$	4.62932	−	17.2769i	0.198846	−	0.742104i
$543$	2.35513	−	8.78945i	0.101068	−	0.377191i
$544$	−2.06220	+	3.57183i	−0.0884160	+	0.153141i
$545$	2.25468	−	2.38221i	0.0965798	−	0.102043i
$546$	4.42314	−	4.96788i	0.189293	−	0.212606i
$547$	27.8171	−	27.8171i	1.18937	−	1.18937i	0.212132	−	0.977241i	$-0.431959\pi$
$547$	27.8171	−	27.8171i	1.18937	−	1.18937i	0.977241	−	0.212132i	$-0.0680407\pi$
$548$	−2.56800	+	0.688094i	−0.109700	+	0.0293939i
$549$	4.09597	+	7.09442i	0.174812	+	0.302783i
$550$	−4.67596	+	22.2870i	−0.199384	+	0.950321i
$551$	−5.09127	−	2.93945i	−0.216896	−	0.125225i
$552$	−5.69431	−	5.69431i	−0.242366	−	0.242366i
$553$	5.60062	−	11.1452i	0.238163	−	0.473941i
$554$		−	14.7464i		−	0.626512i
$555$	7.29489	+	24.5086i	0.309651	+	1.04033i
$556$	−3.96700	+	2.29035i	−0.168238	+	0.0971324i
$557$	−1.36512	−	0.365782i	−0.0578419	−	0.0154987i	0.229782	−	0.973242i	$-0.426199\pi$
$557$	−1.36512	−	0.365782i	−0.0578419	−	0.0154987i	−0.287624	+	0.957743i	$0.592865\pi$
$558$	1.00777	+	3.76106i	0.0426625	+	0.159218i
$559$	1.30577			0.0552282
$560$	5.82431	+	1.03797i	0.246122	+	0.0438622i
$561$	18.7843			0.793076
$562$	0.152031	+	0.567387i	0.00641303	+	0.0239338i
$563$	36.9530	+	9.90152i	1.55738	+	0.417299i	0.931834	−	0.362886i	$-0.118209\pi$
$563$	36.9530	+	9.90152i	1.55738	+	0.417299i	0.625548	+	0.780185i	$0.284875\pi$
$564$	4.37376	−	2.52519i	0.184168	−	0.106330i
$565$	19.7130	+	10.6697i	0.829332	+	0.448878i
$566$			18.6151i			0.782453i
$567$	−2.21084	+	1.45334i	−0.0928464	+	0.0610346i
$568$	4.72632	+	4.72632i	0.198312	+	0.198312i
$569$	−31.1820	−	18.0029i	−1.30722	−	0.754723i	−0.325587	−	0.945512i	$-0.605562\pi$
$569$	−31.1820	−	18.0029i	−1.30722	−	0.754723i	−0.981631	+	0.190789i	$0.938895\pi$
$570$	−8.21947	−	1.96188i	−0.344276	−	0.0821741i
$571$	17.1990	+	29.7895i	0.719756	+	1.24665i	0.961096	+	0.276213i	$0.0890795\pi$
$571$	17.1990	+	29.7895i	0.719756	+	1.24665i	−0.241341	+	0.970440i	$0.577587\pi$
$572$	−11.0601	+	2.96354i	−0.462445	+	0.123912i
$573$	12.8737	−	12.8737i	0.537806	−	0.537806i
$574$	9.46346	+	28.5817i	0.394997	+	1.19298i
$575$	−26.8636	+	29.9934i	−1.12029	+	1.25081i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−11.5727	+	43.1900i	−0.481779	+	1.79802i	0.112370	+	0.993666i	$0.464156\pi$
$577$	−11.5727	+	43.1900i	−0.481779	+	1.79802i	−0.594148	+	0.804355i	$0.702511\pi$
$578$	0.00275276	−	0.0102734i	0.000114500	−	0.000427319i
$579$	5.03564	−	8.72198i	0.209274	−	0.362473i
$580$	2.52636	+	2.39111i	0.104901	+	0.0992854i
$581$	−8.99048	−	8.00466i	−0.372988	−	0.332089i
$582$	0.462652	−	0.462652i	0.0191775	−	0.0191775i
$583$	−37.1066	+	9.94267i	−1.53680	+	0.411783i
$584$	2.17449	+	3.76633i	0.0899811	+	0.155852i
$585$	4.78937	−	2.94361i	0.198016	−	0.121703i
$586$	−25.3199	−	14.6185i	−1.04596	−	0.603883i
$587$	19.7182	+	19.7182i	0.813859	+	0.813859i	0.985210	−	0.171351i	$-0.0548132\pi$
$587$	19.7182	+	19.7182i	0.813859	+	0.813859i	−0.171351	+	0.985210i	$0.554813\pi$
$588$	−6.50665	+	2.58137i	−0.268330	+	0.106454i
$589$		−	14.7149i		−	0.606316i
$590$	0.471540	−	0.871201i	0.0194130	−	0.0358668i
$591$	−19.8946	+	11.4862i	−0.818356	+	0.472478i
$592$	−11.0461	−	2.95980i	−0.453994	−	0.121647i
$593$	−2.57961	−	9.62724i	−0.105932	−	0.395343i	0.892517	−	0.451013i	$-0.148937\pi$
$593$	−2.57961	−	9.62724i	−0.105932	−	0.395343i	−0.998449	+	0.0556699i	$0.982271\pi$
$594$	4.55445			0.186871
$595$	−24.3112	+	2.08216i	−0.996664	+	0.0853604i
$596$	−17.2441			−0.706344
$597$	6.57319	+	24.5315i	0.269023	+	1.00401i
$598$	−19.5559	−	5.23999i	−0.799701	−	0.214279i
$599$	14.2556	−	8.23048i	0.582469	−	0.336288i	−0.179645	−	0.983731i	$-0.557495\pi$
$599$	14.2556	−	8.23048i	0.582469	−	0.336288i	0.762114	+	0.647443i	$0.224162\pi$
$600$	4.46099	+	2.25822i	0.182119	+	0.0921913i
$601$			34.0216i			1.38777i	0.720086	+	0.693885i	$0.244102\pi$
$601$			34.0216i			1.38777i	−0.720086	+	0.693885i	$0.755898\pi$
$602$	−1.22785	−	0.617012i	−0.0500434	−	0.0251475i
$603$	−6.58705	−	6.58705i	−0.268246	−	0.268246i
$604$	−4.82177	−	2.78385i	−0.196195	−	0.113273i
$605$	−5.05795	+	21.1907i	−0.205635	+	0.861525i
$606$	2.80102	+	4.85151i	0.113784	+	0.197079i
$607$	34.7707	−	9.31678i	1.41130	−	0.378156i	0.528910	−	0.848678i	$-0.322601\pi$
$607$	34.7707	−	9.31678i	1.41130	−	0.378156i	0.882389	+	0.470521i	$0.155934\pi$
$608$	2.67224	−	2.67224i	0.108374	−	0.108374i
$609$	−4.03058	−	0.833240i	−0.163327	−	0.0337646i
$610$	0.503605	+	18.3108i	0.0203904	+	0.741383i
$611$	6.34852	−	10.9960i	0.256833	−	0.444849i
$612$	1.06747	−	3.98386i	0.0431500	−	0.161038i
$613$	−8.52125	+	31.8017i	−0.344170	+	1.28446i	0.549409	+	0.835554i	$0.314853\pi$
$613$	−8.52125	+	31.8017i	−0.344170	+	1.28446i	−0.893579	+	0.448906i	$0.851814\pi$
$614$	1.15586	−	2.00201i	0.0466469	−	0.0807947i
$615$	0.699571	+	25.4360i	0.0282094	+	1.02568i
$616$	11.8004	+	2.43950i	0.475452	+	0.0982901i
$617$	−10.3705	+	10.3705i	−0.417499	+	0.417499i	−0.884341	−	0.466842i	$-0.845392\pi$
$617$	−10.3705	+	10.3705i	−0.417499	+	0.417499i	0.466842	+	0.884341i	$0.345392\pi$
$618$	−5.36863	+	1.43852i	−0.215958	+	0.0578658i
$619$	−2.58828	−	4.48304i	−0.104032	−	0.180188i	0.809310	−	0.587381i	$-0.199841\pi$
$619$	−2.58828	−	4.48304i	−0.104032	−	0.180188i	−0.913342	+	0.407193i	$0.866508\pi$
$620$	−2.02138	+	8.46877i	−0.0811808	+	0.340114i
$621$	6.97408	+	4.02648i	0.279860	+	0.161577i
$622$	9.81743	+	9.81743i	0.393643	+	0.393643i
$623$	14.2990	+	7.18544i	0.572876	+	0.287879i
$624$			2.51408i			0.100644i
$625$	10.0480	−	22.8919i	0.401921	−	0.915674i
$626$	−11.6830	+	6.74520i	−0.466948	+	0.269592i
$627$	−16.6253	−	4.45474i	−0.663951	−	0.177905i
$628$	−1.06916	−	3.99014i	−0.0426640	−	0.159224i
$629$	47.1658			1.88062
$630$	−5.89450	+	0.504841i	−0.234843	+	0.0201134i
$631$	14.5385			0.578769			0.289384	−	0.957213i	$-0.406549\pi$
$631$	14.5385			0.578769			0.289384	+	0.957213i	$0.406549\pi$
$632$	1.22019	+	4.55381i	0.0485365	+	0.181141i
$633$	13.1542	+	3.52466i	0.522832	+	0.140093i
$634$	−11.8793	+	6.85853i	−0.471788	+	0.272387i
$635$	19.4442	−	35.9245i	0.771621	−	1.42562i
$636$			8.43473i			0.334459i
$637$	−10.9218	+	13.7994i	−0.432736	+	0.546752i
$638$	5.00987	+	5.00987i	0.198343	+	0.198343i
$639$	−5.78854	−	3.34201i	−0.228991	−	0.132208i
$640$	−1.90502	+	1.17085i	−0.0753026	+	0.0462819i
$641$	−20.8743	−	36.1553i	−0.824484	−	1.42805i	−0.902313	−	0.431082i	$-0.858132\pi$
$641$	−20.8743	−	36.1553i	−0.824484	−	1.42805i	0.0778281	−	0.996967i	$-0.475201\pi$
$642$	7.23514	−	1.93865i	0.285548	−	0.0765124i
$643$	−15.5128	+	15.5128i	−0.611766	+	0.611766i	−0.943406	−	0.331640i	$-0.892398\pi$
$643$	−15.5128	+	15.5128i	−0.611766	+	0.611766i	0.331640	+	0.943406i	$0.392398\pi$
$644$	15.9129	+	14.1680i	0.627056	+	0.558298i
$645$	−0.843485	−	0.798330i	−0.0332122	−	0.0314342i
$646$	−7.79328	+	13.4984i	−0.306623	+	0.531086i
$647$	−3.70148	+	13.8141i	−0.145520	+	0.543089i	0.854211	+	0.519926i	$0.174040\pi$
$647$	−3.70148	+	13.8141i	−0.145520	+	0.543089i	−0.999732	+	0.0231633i	$0.992626\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	1.00886	−	1.74740i	0.0396012	−	0.0685913i
$650$	12.5514	−	0.690928i	0.492305	−	0.0271004i
$651$	−3.23809	−	9.77973i	−0.126911	−	0.383298i
$652$	−15.3717	+	15.3717i	−0.602003	+	0.602003i
$653$	−14.7451	+	3.95094i	−0.577021	+	0.154612i	−0.535515	−	0.844526i	$-0.679882\pi$
$653$	−14.7451	+	3.95094i	−0.577021	+	0.154612i	−0.0415062	+	0.999138i	$0.513216\pi$
$654$	−0.733433	−	1.27034i	−0.0286795	−	0.0496743i
$655$	0.812840	+	0.194014i	0.0317603	+	0.00758077i
$656$	−9.85506	−	5.68982i	−0.384775	−	0.222150i
$657$	−3.07520	−	3.07520i	−0.119975	−	0.119975i
$658$	−11.1656	+	7.33993i	−0.435279	+	0.286140i
$659$			18.9116i			0.736690i	0.929689	+	0.368345i	$0.120076\pi$
$659$			18.9116i			0.736690i	−0.929689	+	0.368345i	$0.879924\pi$
$660$	8.95631	+	4.84763i	0.348624	+	0.188694i
$661$	19.5815	−	11.3054i	0.761632	−	0.439728i	−0.0682495	−	0.997668i	$-0.521741\pi$
$661$	19.5815	−	11.3054i	0.761632	−	0.439728i	0.829881	+	0.557940i	$0.188408\pi$
$662$	−32.1061	−	8.60281i	−1.24784	−	0.334358i
$663$	−2.68371	−	10.0157i	−0.104226	−	0.388979i
$664$	4.54978			0.176566
$665$	22.0108	+	3.92261i	0.853540	+	0.152112i
$666$	11.4358			0.443129
$667$	3.24233	+	12.1006i	0.125544	+	0.468535i
$668$	23.8985	+	6.40358i	0.924660	+	0.247762i
$669$	−19.4015	+	11.2014i	−0.750104	+	0.433073i
$670$	−5.94235	−	19.9645i	−0.229573	−	0.771296i
$671$			37.3097i			1.44033i
$672$	1.18797	−	2.36405i	0.0458269	−	0.0911952i
$673$	−24.2623	−	24.2623i	−0.935243	−	0.935243i	0.0627838	−	0.998027i	$-0.480002\pi$
$673$	−24.2623	−	24.2623i	−0.935243	−	0.935243i	−0.998027	+	0.0627838i	$0.980002\pi$
$674$	−20.8610	−	12.0441i	−0.803534	−	0.463921i
$675$	−4.89346	−	1.02668i	−0.188349	−	0.0395169i
$676$	−3.33971	−	5.78455i	−0.128450	−	0.222483i
$677$	8.59870	−	2.30402i	0.330475	−	0.0885505i	−0.0897664	−	0.995963i	$-0.528612\pi$
$677$	8.59870	−	2.30402i	0.330475	−	0.0885505i	0.420241	+	0.907412i	$0.361945\pi$
$678$	7.08834	−	7.08834i	0.272226	−	0.272226i
$679$	−1.15112	+	1.29289i	−0.0441761	+	0.0496166i
$680$	6.33949	−	6.69806i	0.243108	−	0.256859i
$681$	5.47634	−	9.48530i	0.209854	−	0.363477i
$682$	−4.58985	+	17.1296i	−0.175755	+	0.655925i
$683$	12.3979	−	46.2697i	0.474394	−	1.77046i	−0.149299	−	0.988792i	$-0.547702\pi$
$683$	12.3979	−	46.2697i	0.474394	−	1.77046i	0.623693	−	0.781669i	$-0.285632\pi$
$684$	−1.88956	+	3.27281i	−0.0722491	+	0.125139i
$685$	5.94254	−	0.163439i	0.227053	−	0.00624467i
$686$	16.7906	−	7.81510i	0.641068	−	0.298382i
$687$	20.4667	−	20.4667i	0.780854	−	0.780854i
$688$	0.501686	−	0.134426i	0.0191266	−	0.00512496i
$689$	10.6028	+	18.3645i	0.403934	+	0.699633i
$690$	9.42883	+	15.3411i	0.358949	+	0.584025i
$691$	−22.3848	−	12.9239i	−0.851559	−	0.491648i	0.00961738	−	0.999954i	$-0.496939\pi$
$691$	−22.3848	−	12.9239i	−0.851559	−	0.491648i	−0.861177	+	0.508306i	$0.830272\pi$
$692$	11.7140	+	11.7140i	0.445300	+	0.445300i
$693$	−12.0297	+	0.697800i	−0.456971	+	0.0265072i
$694$		−	2.05709i		−	0.0780861i
$695$	9.81711	−	2.92202i	0.372384	−	0.110839i
$696$	1.34721	−	0.777814i	0.0510660	−	0.0294829i
$697$	45.3349	+	12.1474i	1.71718	+	0.460117i
$698$	−3.03467	−	11.3255i	−0.114864	−	0.428677i
$699$	1.41209			0.0534102
$700$	−12.1289	−	5.28117i	−0.458428	−	0.199610i
$701$	3.95788			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$701$	3.95788			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$702$	−0.650691	−	2.42841i	−0.0245587	−	0.0916544i
$703$	−41.7447	−	11.1854i	−1.57443	−	0.421867i
$704$	−3.94427	+	2.27722i	−0.148655	+	0.0858261i
$705$	−10.8237	+	3.22163i	−0.407644	+	0.121334i
$706$		−	11.4227i		−	0.429897i
$707$	−8.14167	−	12.3852i	−0.306199	−	0.465793i
$708$	−0.313264	−	0.313264i	−0.0117732	−	0.0117732i
$709$	−25.1665	−	14.5299i	−0.945148	−	0.545682i	−0.0535778	−	0.998564i	$-0.517063\pi$
$709$	−25.1665	−	14.5299i	−0.945148	−	0.545682i	−0.891570	+	0.452882i	$0.850396\pi$
$710$	−7.82600	−	12.7332i	−0.293704	−	0.477869i
$711$	−2.35722	−	4.08283i	−0.0884028	−	0.153118i
$712$	−5.84241	+	1.56547i	−0.218954	+	0.0586684i
$713$	−22.1722	+	22.1722i	−0.830354	+	0.830354i
$714$	−2.20915	+	10.6862i	−0.0826753	+	0.399920i
$715$	25.5938	−	0.703911i	0.957154	−	0.0263248i
$716$	6.36367	−	11.0222i	0.237821	−	0.411919i
$717$	−1.12956	+	4.21559i	−0.0421843	+	0.157434i
$718$	−0.624155	+	2.32938i	−0.0232932	+	0.0869316i
$719$	−10.1319	+	17.5490i	−0.377857	+	0.654467i	−0.990750	−	0.135699i	$-0.956672\pi$
$719$	−10.1319	+	17.5490i	−0.377857	+	0.654467i	0.612893	+	0.790166i	$0.290005\pi$
$720$	1.53707	−	1.62401i	0.0572833	−	0.0605233i
$721$	13.9598	−	4.62212i	0.519891	−	0.172137i
$722$	−3.33633	+	3.33633i	−0.124165	+	0.124165i
$723$	2.96531	−	0.794551i	0.110281	−	0.0295497i
$724$	−4.54975	−	7.88040i	−0.169090	−	0.292873i
$725$	−4.25343	−	6.51212i	−0.157969	−	0.241854i
$726$	8.43768	+	4.87150i	0.313152	+	0.180798i
$727$	−2.80940	−	2.80940i	−0.104195	−	0.104195i	0.653088	−	0.757282i	$-0.273473\pi$
$727$	−2.80940	−	2.80940i	−0.104195	−	0.104195i	−0.757282	+	0.653088i	$0.773473\pi$
$728$	−0.385189	−	6.64046i	−0.0142760	−	0.246112i
$729$			1.00000i			0.0370370i
$730$	−2.77421	−	9.32052i	−0.102678	−	0.344968i
$731$	−1.85515	+	1.07107i	−0.0686152	+	0.0396150i
$732$	7.91280	+	2.12023i	0.292466	+	0.0783659i
$733$	−0.451275	−	1.68418i	−0.0166682	−	0.0622066i	0.957091	−	0.289788i	$-0.0935848\pi$
$733$	−0.451275	−	1.68418i	−0.0166682	−	0.0622066i	−0.973759	+	0.227582i	$0.926918\pi$
$734$	5.20884			0.192262
$735$	15.4919	−	2.23656i	0.571426	−	0.0824966i
$736$	−8.05297			−0.296836
$737$	−10.9809	−	40.9813i	−0.404487	−	1.50957i
$738$	10.9919	+	2.94527i	0.404617	+	0.108417i
$739$	−20.2692	+	11.7024i	−0.745615	+	0.430481i	−0.824107	−	0.566434i	$-0.808323\pi$
$739$	−20.2692	+	11.7024i	−0.745615	+	0.430481i	0.0784926	+	0.996915i	$0.474989\pi$
$740$	22.4885	+	12.1720i	0.826693	+	0.447450i
$741$			9.50098i			0.349027i
$742$	−1.29231	−	22.2787i	−0.0474421	−	0.817879i
$743$	1.84057	+	1.84057i	0.0675240	+	0.0675240i	0.740062	−	0.672538i	$-0.234796\pi$
$743$	1.84057	+	1.84057i	0.0675240	+	0.0675240i	−0.672538	+	0.740062i	$0.734796\pi$
$744$	3.37208	+	1.94687i	0.123626	+	0.0713757i
$745$	37.5053	+	8.95203i	1.37409	+	0.327977i
$746$	0.0733279	+	0.127008i	0.00268472	+	0.00465008i
$747$	−4.39475	+	1.17757i	−0.160795	+	0.0430850i
$748$	13.2825	−	13.2825i	0.485658	−	0.485658i
$749$	−18.8132	+	6.22909i	−0.687420	+	0.227606i
$750$	−8.53020	−	7.22742i	−0.311479	−	0.263908i
$751$	−21.1862	+	36.6956i	−0.773096	+	1.33904i	0.162762	+	0.986665i	$0.447960\pi$
$751$	−21.1862	+	36.6956i	−0.773096	+	1.33904i	−0.935858	+	0.352376i	$0.885374\pi$
$752$	1.30713	−	4.87829i	0.0476663	−	0.177893i
$753$	−0.324443	+	1.21084i	−0.0118234	+	0.0441254i
$754$	1.95548	−	3.38699i	0.0712145	−	0.123347i
$755$	9.04201	+	8.55795i	0.329072	+	0.311456i
$756$	−0.535629	+	2.59097i	−0.0194807	+	0.0942325i
$757$	10.2470	−	10.2470i	0.372434	−	0.372434i	−0.495929	−	0.868363i	$-0.665172\pi$
$757$	10.2470	−	10.2470i	0.372434	−	0.372434i	0.868363	+	0.495929i	$0.165172\pi$
$758$	−17.9119	+	4.79948i	−0.650590	+	0.174325i
$759$	18.3384	+	31.7631i	0.665642	+	1.15293i
$760$	−7.19930	+	4.42478i	−0.261146	+	0.160504i
$761$	13.4082	+	7.74124i	0.486048	+	0.280620i	0.722933	−	0.690918i	$-0.242793\pi$
$761$	13.4082	+	7.74124i	0.486048	+	0.280620i	−0.236886	+	0.971538i	$0.576127\pi$
$762$	−12.9176	−	12.9176i	−0.467956	−	0.467956i
$763$	2.13186	+	3.24300i	0.0771784	+	0.117404i
$764$		−	18.2062i		−	0.658676i
$765$	−4.38989	+	8.11061i	−0.158717	+	0.293240i
$766$	3.33386	−	1.92480i	0.120457	−	0.0695460i
$767$	−1.07584	−	0.288270i	−0.0388463	−	0.0104088i
$768$	0.258819	+	0.965926i	0.00933933	+	0.0348548i
$769$	15.9644			0.575691			0.287846	−	0.957677i	$-0.407061\pi$
$769$	15.9644			0.575691			0.287846	+	0.957677i	$0.407061\pi$
$770$	−24.3991	−	11.4319i	−0.879283	−	0.411976i
$771$	−7.05834			−0.254200
$772$	−2.60664	−	9.72810i	−0.0938149	−	0.350122i
$773$	22.3797	+	5.99662i	0.804941	+	0.215683i	0.637752	−	0.770241i	$-0.279864\pi$
$773$	22.3797	+	5.99662i	0.804941	+	0.215683i	0.167189	+	0.985925i	$0.446531\pi$
$774$	−0.449799	+	0.259692i	−0.0161677	+	0.00933443i
$775$	8.79290	−	17.3699i	0.315850	−	0.623947i
$776$		−	0.654289i		−	0.0234876i
$777$	−30.2055	+	1.75211i	−1.08362	+	0.0628567i
$778$	−12.6018	−	12.6018i	−0.451798	−	0.451798i
$779$	−37.2434	−	21.5025i	−1.33438	−	0.770406i
$780$	1.30515	−	5.46804i	0.0467319	−	0.195787i
$781$	−15.2210	−	26.3636i	−0.544651	−	0.943363i
$782$	32.0819	−	8.59632i	1.14725	−	0.307404i
$783$	−1.09999	+	1.09999i	−0.0393106	+	0.0393106i
$784$	−2.77559	+	6.42620i	−0.0991284	+	0.229507i
$785$	0.253950	+	9.23348i	0.00906386	+	0.329557i
$786$	0.186862	−	0.323655i	0.00666516	−	0.0115444i
$787$	−0.544910	+	2.03363i	−0.0194239	+	0.0724912i	−0.974958	−	0.222391i	$-0.928614\pi$
$787$	−0.544910	+	2.03363i	−0.0194239	+	0.0724912i	0.955534	+	0.294882i	$0.0952805\pi$
$788$	−5.94568	+	22.1896i	−0.211806	+	0.790471i
$789$	2.84395	−	4.92586i	0.101247	−	0.175365i
$790$	−0.289824	−	10.5378i	−0.0103115	−	0.374920i
$791$	−17.6365	+	19.8085i	−0.627081	+	0.704310i
$792$	3.22048	−	3.22048i	0.114435	−	0.114435i
$793$	19.8934	−	5.33042i	0.706435	−	0.189289i
$794$	12.8232	+	22.2105i	0.455079	+	0.788219i
$795$	4.37878	−	18.3453i	0.155299	−	0.650640i
$796$	21.9943	+	12.6984i	0.779569	+	0.450084i
$797$	−23.6759	−	23.6759i	−0.838642	−	0.838642i	0.150038	−	0.988680i	$-0.452060\pi$
$797$	−23.6759	−	23.6759i	−0.838642	−	0.838642i	−0.988680	+	0.150038i	$0.952060\pi$
$798$	4.48947	−	8.93402i	0.158926	−	0.316261i
$799$			20.8298i			0.736904i
$800$	4.75120	−	1.55760i	0.167980	−	0.0550694i
$801$	5.23816	−	3.02425i	0.185081	−	0.106857i
$802$	5.08192	+	1.36170i	0.179449	+	0.0480832i
$803$	−5.12649	−	19.1323i	−0.180910	−	0.675164i
$804$	−9.31550			−0.328532
$805$	−27.2549	−	39.0760i	−0.960610	−	1.37725i
$806$	9.78915			0.344808
$807$	−1.99493	−	7.44518i	−0.0702249	−	0.262083i
$808$	5.41115	+	1.44991i	0.190364	+	0.0510078i
$809$	1.15441	−	0.666500i	0.0405869	−	0.0234329i	−0.479569	−	0.877504i	$-0.659207\pi$
$809$	1.15441	−	0.666500i	0.0405869	−	0.0234329i	0.520156	+	0.854071i	$0.325874\pi$
$810$	−1.06437	+	1.96650i	−0.0373982	+	0.0690957i
$811$		−	41.6705i		−	1.46325i	−0.681708	−	0.731624i	$-0.738763\pi$
$811$		−	41.6705i		−	1.46325i	0.681708	−	0.731624i	$-0.261237\pi$
$812$	−3.43924	+	2.26086i	−0.120694	+	0.0793406i
$813$	12.6475	+	12.6475i	0.443568	+	0.443568i
$814$	45.1059	+	26.0419i	1.58096	+	0.912768i
$815$	41.4131	−	25.4530i	1.45064	−	0.891580i
$816$	−2.06220	−	3.57183i	−0.0721914	−	0.125039i
$817$	1.89593	−	0.508013i	0.0663302	−	0.0177731i
$818$	5.92234	−	5.92234i	0.207070	−	0.207070i
$819$	2.09074	+	6.31449i	0.0730564	+	0.220646i
$820$	18.4807	+	17.4913i	0.645373	+	0.610823i
$821$	16.0833	−	27.8571i	0.561312	−	0.972221i	−0.436070	−	0.899913i	$-0.643630\pi$
$821$	16.0833	−	27.8571i	0.561312	−	0.972221i	0.997382	−	0.0723083i	$-0.0230366\pi$
$822$	0.688094	−	2.56800i	0.0240000	−	0.0895693i
$823$	3.82988	−	14.2933i	0.133501	−	0.498233i	−0.866498	−	0.499180i	$-0.833635\pi$
$823$	3.82988	−	14.2933i	0.133501	−	0.498233i	1.00000		0.000946758i	$0.000301363\pi$
$824$	−2.77901	+	4.81338i	−0.0968113	+	0.167682i
$825$	−16.9631	−	15.1930i	−0.590580	−	0.528952i
$826$	0.875423	+	0.779431i	0.0304599	+	0.0271199i
$827$	−34.2632	+	34.2632i	−1.19145	+	1.19145i	−0.214788	+	0.976661i	$0.568906\pi$
$827$	−34.2632	+	34.2632i	−1.19145	+	1.19145i	−0.976661	+	0.214788i	$0.931094\pi$
$828$	7.77857	−	2.08426i	0.270324	−	0.0724331i
$829$	25.2456	+	43.7267i	0.876817	+	1.51869i	0.854814	+	0.518934i	$0.173671\pi$
$829$	25.2456	+	43.7267i	0.876817	+	1.51869i	0.0220025	+	0.999758i	$0.492996\pi$
$830$	−9.89563	−	2.36196i	−0.343482	−	0.0819848i
$831$	12.7707	+	7.37318i	0.443011	+	0.255773i
$832$	1.77772	+	1.77772i	0.0616313	+	0.0616313i
$833$	4.19779	−	28.5640i	0.145445	−	0.989682i
$834$		−	4.58070i		−	0.158617i
$835$	−48.6541	−	26.3342i	−1.68375	−	0.911332i
$836$	−14.9058	+	8.60589i	−0.515529	+	0.297641i
$837$	−3.76106	−	1.00777i	−0.130001	−	0.0348338i
$838$	−2.46675	−	9.20603i	−0.0852124	−	0.318017i
$839$	−22.4313			−0.774414			−0.387207	−	0.921993i	$-0.626560\pi$
$839$	−22.4313			−0.774414			−0.387207	+	0.921993i	$0.626560\pi$
$840$	−3.81106	+	4.52502i	−0.131494	+	0.156128i
$841$	26.5800			0.916553
$842$	4.36008	+	16.2721i	0.150258	+	0.560772i
$843$	−0.567387	−	0.152031i	−0.0195418	−	0.00523622i
$844$	11.7937	−	6.80911i	0.405957	−	0.234379i
$845$	4.26080	+	14.3150i	0.146576	+	0.492451i
$846$			5.05038i			0.173636i
$847$	−23.0329	−	11.5744i	−0.791420	−	0.397700i
$848$	5.96425	+	5.96425i	0.204813	+	0.204813i
$849$	−16.1212	−	9.30757i	−0.553278	−	0.319435i
$850$	−17.2654	+	11.2770i	−0.592199	+	0.386799i
$851$	46.0461	+	79.7542i	1.57844	+	2.73394i
$852$	−6.45627	+	1.72995i	−0.221188	+	0.0592672i
$853$	24.4497	−	24.4497i	0.837140	−	0.837140i	−0.151341	−	0.988482i	$-0.548359\pi$
$853$	24.4497	−	24.4497i	0.837140	−	0.837140i	0.988482	+	0.151341i	$0.0483592\pi$
$854$	−21.2250	−	4.38784i	−0.726305	−	0.150149i
$855$	5.80877	−	6.13733i	0.198656	−	0.209892i
$856$	3.74518	−	6.48684i	0.128008	−	0.221716i
$857$	3.75655	−	14.0196i	0.128321	−	0.478901i	−0.871615	−	0.490191i	$-0.836927\pi$
$857$	3.75655	−	14.0196i	0.128321	−	0.478901i	0.999936	+	0.0112896i	$0.00359368\pi$
$858$	2.96354	−	11.0601i	0.101173	−	0.377585i
$859$	8.65502	−	14.9909i	0.295306	−	0.511484i	−0.679750	−	0.733444i	$-0.737912\pi$
$859$	8.65502	−	14.9909i	0.295306	−	0.511484i	0.975056	+	0.221959i	$0.0712452\pi$
$860$	−1.16094	+	0.0319295i	−0.0395877	+	0.00108879i
$861$	−29.4842	−	6.09527i	−1.00482	−	0.207726i
$862$	15.2439	−	15.2439i	0.519209	−	0.519209i
$863$	9.04469	−	2.42352i	0.307885	−	0.0824975i	−0.101568	−	0.994829i	$-0.532386\pi$
$863$	9.04469	−	2.42352i	0.307885	−	0.0824975i	0.409453	+	0.912331i	$0.365719\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−19.3965	−	31.5588i	−0.659500	−	1.07303i
$866$	−31.6992	−	18.3016i	−1.07718	−	0.621912i
$867$	0.00752068	+	0.00752068i	0.000255416	+	0.000255416i
$868$	−9.20499	−	4.62564i	−0.312438	−	0.157005i
$869$		−	21.4717i		−	0.728378i
$870$	−3.33394	+	0.992333i	−0.113031	+	0.0336432i
$871$	−20.2822	+	11.7099i	−0.687236	+	0.396776i
$872$	−1.41688	−	0.379653i	−0.0479817	−	0.0128567i
$873$	0.169342	+	0.631994i	0.00573137	+	0.0213898i
$874$	−30.4331			−1.02942
$875$	23.6383	+	17.7829i	0.799119	+	0.601173i
$876$	−4.34898			−0.146939
$877$	−9.68626	−	36.1496i	−0.327082	−	1.22069i	−0.912202	−	0.409740i	$-0.865619\pi$
$877$	−9.68626	−	36.1496i	−0.327082	−	1.22069i	0.585120	−	0.810946i	$-0.301047\pi$
$878$	−20.4580	−	5.48171i	−0.690425	−	0.184999i
$879$	25.3199	−	14.6185i	0.854020	−	0.493069i
$880$	9.76086	−	2.90528i	0.329038	−	0.0979369i
$881$			49.1425i			1.65565i	0.560984	+	0.827827i	$0.310423\pi$
$881$			49.1425i			1.65565i	−0.560984	+	0.827827i	$0.689577\pi$
$882$	1.01780	−	6.92561i	0.0342709	−	0.233197i
$883$	22.9167	+	22.9167i	0.771207	+	0.771207i	0.978318	−	0.207110i	$-0.0664060\pi$
$883$	22.9167	+	22.9167i	0.771207	+	0.771207i	−0.207110	+	0.978318i	$0.566406\pi$
$884$	−8.97985	−	5.18452i	−0.302025	−	0.174374i
$885$	0.518713	+	0.843966i	0.0174363	+	0.0283696i
$886$	2.07519	+	3.59433i	0.0697173	+	0.120754i
$887$	−25.3392	+	6.78961i	−0.850806	+	0.227973i	−0.657770	−	0.753219i	$-0.728500\pi$
$887$	−25.3392	+	6.78961i	−0.850806	+	0.227973i	−0.193036	+	0.981192i	$0.561833\pi$
$888$	8.08634	−	8.08634i	0.271360	−	0.271360i
$889$	36.0986	+	32.1403i	1.21071	+	1.07795i
$890$	13.5198	−	0.371836i	0.453184	−	0.0124640i
$891$	−2.27722	+	3.94427i	−0.0762899	+	0.132138i
$892$	−5.79830	+	21.6395i	−0.194141	+	0.724545i
$893$	4.93981	−	18.4356i	0.165304	−	0.616925i
$894$	8.62203	−	14.9338i	0.288364	−	0.499461i
$895$	−19.5628	+	20.6693i	−0.653913	+	0.690899i
$896$	−0.831614	−	2.51166i	−0.0277823	−	0.0839086i
$897$	14.3159	−	14.3159i	0.477995	−	0.477995i
$898$	−28.3785	+	7.60399i	−0.947002	+	0.253748i
$899$	−3.02860	−	5.24569i	−0.101010	−	0.174954i
$900$	−4.18617	+	2.73423i	−0.139539	+	0.0911408i
$901$	−30.1274	−	17.3941i	−1.00369	−	0.579481i
$902$	36.6479	+	36.6479i	1.22024	+	1.22024i
$903$	1.14827	−	0.754842i	0.0382121	−	0.0251196i
$904$		−	10.0244i		−	0.333407i
$905$	5.80457	+	19.5016i	0.192950	+	0.648255i
$906$	4.82177	−	2.78385i	0.160193	−	0.0924872i
$907$	−1.22193	−	0.327416i	−0.0405736	−	0.0108717i	0.238475	−	0.971149i	$-0.423352\pi$
$907$	−1.22193	−	0.327416i	−0.0405736	−	0.0108717i	−0.279049	+	0.960277i	$0.590019\pi$
$908$	−2.83476	−	10.5795i	−0.0940749	−	0.351092i
$909$	−5.60204			−0.185808
$910$	−2.60953	+	14.6428i	−0.0865052	+	0.485403i
$911$	−49.7996			−1.64993			−0.824967	−	0.565182i	$-0.808806\pi$
$911$	−49.7996			−1.64993			−0.824967	+	0.565182i	$0.808806\pi$
$912$	0.978107	+	3.65035i	0.0323884	+	0.120875i
$913$	−20.0156	−	5.36318i	−0.662421	−	0.177495i
$914$	0.408203	−	0.235676i	0.0135021	−	0.00779547i
$915$	−16.1094	−	8.71927i	−0.532561	−	0.288250i
$916$		−	28.9443i		−	0.956347i
$917$	−0.443974	+	0.883504i	−0.0146613	+	0.0291759i
$918$	2.91639	+	2.91639i	0.0962551	+	0.0962551i
$919$	43.6221	+	25.1852i	1.43896	+	0.830784i	0.997777	−	0.0666338i	$-0.0212259\pi$
$919$	43.6221	+	25.1852i	1.43896	+	0.830784i	0.441182	+	0.897418i	$0.354559\pi$
$920$	17.5150	+	4.18060i	0.577452	+	0.137830i
$921$	1.15586	+	2.00201i	0.0380870	+	0.0659686i
$922$	25.4231	−	6.81209i	0.837264	−	0.224344i
$923$	−11.8823	+	11.8823i	−0.391112	+	0.391112i
$924$	−8.01287	+	8.99971i	−0.263604	+	0.296069i
$925$	−42.5929	−	38.1482i	−1.40045	−	1.25431i
$926$	0.725623	−	1.25682i	0.0238455	−	0.0413015i
$927$	1.43852	−	5.36863i	0.0472472	−	0.176329i
$928$	0.402626	−	1.50262i	0.0132168	−	0.0493259i
$929$	11.4115	−	19.7652i	0.374398	−	0.648476i	−0.615839	−	0.787872i	$-0.711183\pi$
$929$	11.4115	−	19.7652i	0.374398	−	0.648476i	0.990237	+	0.139396i	$0.0445161\pi$
$930$	−6.32347	−	5.98495i	−0.207355	−	0.196254i
$931$	−10.4893	+	24.2854i	−0.343773	+	0.795921i
$932$	0.998499	−	0.998499i	0.0327069	−	0.0327069i
$933$	−13.4109	+	3.59343i	−0.439052	+	0.117644i
$934$	−15.5068	−	26.8586i	−0.507399	−	0.878841i
$935$	−35.7846	+	21.9937i	−1.17028	+	0.719270i
$936$	−2.17725	−	1.25704i	−0.0711658	−	0.0410876i
$937$	−24.9461	−	24.9461i	−0.814954	−	0.814954i	0.170418	−	0.985372i	$-0.445488\pi$
$937$	−24.9461	−	24.9461i	−0.814954	−	0.814954i	−0.985372	+	0.170418i	$0.945488\pi$
$938$	24.6051	−	1.42725i	0.803386	−	0.0466015i
$939$		−	13.4904i		−	0.440242i
$940$	−5.37548	+	9.93156i	−0.175329	+	0.323932i
$941$	−16.1409	+	9.31896i	−0.526179	+	0.303789i	−0.739459	−	0.673202i	$-0.764919\pi$
$941$	−16.1409	+	9.31896i	−0.526179	+	0.303789i	0.213280	+	0.976991i	$0.431585\pi$
$942$	3.99014	+	1.06916i	0.130006	+	0.0348350i
$943$	23.7181	+	88.5173i	0.772369	+	2.88252i
$944$	−0.443022			−0.0144191
$945$	2.51004	−	5.35721i	0.0816518	−	0.174270i
$946$	−2.36551			−0.0769092
$947$	0.657006	+	2.45198i	0.0213498	+	0.0796786i	0.975779	−	0.218760i	$-0.0702010\pi$
$947$	0.657006	+	2.45198i	0.0213498	+	0.0796786i	−0.954429	+	0.298438i	$0.903534\pi$
$948$	−4.55381	−	1.22019i	−0.147901	−	0.0396299i
$949$	−9.46884	+	5.46684i	−0.307372	+	0.177461i
$950$	17.9553	−	5.88634i	0.582548	−	0.190978i
$951$		−	13.7171i		−	0.444806i
$952$	5.99416	+	9.11836i	0.194272	+	0.295528i
$953$	31.1031	+	31.1031i	1.00753	+	1.00753i	0.999971	+	0.00755624i	$0.00240525\pi$
$953$	31.1031	+	31.1031i	1.00753	+	1.00753i	0.00755624	+	0.999971i	$0.497595\pi$
$954$	−7.30469	−	4.21737i	−0.236498	−	0.136542i
$955$	−9.45149	+	39.5979i	−0.305843	+	1.28136i
$956$	2.18215	+	3.77959i	0.0705758	+	0.122241i
$957$	−6.84361	+	1.83374i	−0.221222	+	0.0592764i
$958$	23.5834	−	23.5834i	0.761945	−	0.761945i
$959$	−1.42402	+	6.88831i	−0.0459840	+	0.222435i
$960$	−0.0614757	−	2.23522i	−0.00198412	−	0.0721415i
$961$	−7.91940	+	13.7168i	−0.255465	+	0.442477i
$962$	7.44117	−	27.7708i	0.239913	−	0.895368i
$963$	−1.93865	+	7.23514i	−0.0624721	+	0.233149i
$964$	1.53496	−	2.65862i	0.0494376	−	0.0856284i
$965$	0.619139	+	22.5115i	0.0199308	+	0.724672i
$966$	−20.2263	+	6.69696i	−0.650770	+	0.215471i
$967$	−14.7707	+	14.7707i	−0.474993	+	0.474993i	−0.903526	−	0.428533i	$-0.859031\pi$
$967$	−14.7707	+	14.7707i	−0.474993	+	0.474993i	0.428533	+	0.903526i	$0.359031\pi$
$968$	9.41101	−	2.52167i	0.302481	−	0.0810496i
$969$	−7.79328	−	13.4984i	−0.250356	−	0.433630i
$970$	−0.339666	+	1.42306i	−0.0109060	+	0.0456917i
$971$	9.39194	+	5.42244i	0.301402	+	0.174014i	0.643072	−	0.765805i	$-0.277659\pi$
$971$	9.39194	+	5.42244i	0.301402	+	0.174014i	−0.341671	+	0.939820i	$0.610993\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	0.701821	+	12.0990i	0.0224994	+	0.387878i
$974$			3.30368i			0.105857i
$975$	−5.67733	+	11.2153i	−0.181820	+	0.359176i
$976$	7.09442	−	4.09597i	0.227087	−	0.131109i
$977$	−16.5560	−	4.43616i	−0.529673	−	0.141925i	−0.0159356	−	0.999873i	$-0.505073\pi$
$977$	−16.5560	−	4.43616i	−0.529673	−	0.141925i	−0.513737	+	0.857948i	$0.671739\pi$
$978$	−5.62644	−	20.9982i	−0.179914	−	0.671447i
$979$	27.5476			0.880426
$980$	9.37292	−	12.5359i	0.299407	−	0.400444i
$981$	1.46687			0.0468334
$982$	0.936018	+	3.49327i	0.0298695	+	0.111475i
$983$	−1.62331	−	0.434966i	−0.0517757	−	0.0138732i	0.232838	−	0.972515i	$-0.425199\pi$
$983$	−1.62331	−	0.434966i	−0.0517757	−	0.0138732i	−0.284614	+	0.958642i	$0.591865\pi$
$984$	9.85506	−	5.68982i	0.314168	−	0.181385i
$985$	24.4511	−	45.1751i	0.779077	−	1.43940i
$986$			6.41602i			0.204328i
$987$	−0.773782	−	13.3396i	−0.0246298	−	0.424605i
$988$	6.71821	+	6.71821i	0.213735	+	0.213735i
$989$	−3.62222	−	2.09129i	−0.115180	−	0.0664992i
$990$	−8.67632	+	5.33258i	−0.275752	+	0.169480i
$991$	8.40392	+	14.5560i	0.266959	+	0.462387i	0.968075	−	0.250660i	$-0.0806478\pi$
$991$	8.40392	+	14.5560i	0.266959	+	0.462387i	−0.701116	+	0.713047i	$0.747314\pi$
$992$	3.76106	−	1.00777i	0.119414	−	0.0319968i
$993$	23.5033	−	23.5033i	0.745855	−	0.745855i
$994$	16.7880	−	5.55853i	0.532482	−	0.176306i
$995$	−41.2448	−	39.0368i	−1.30755	−	1.23755i
$996$	−2.27489	+	3.94022i	−0.0720826	+	0.124851i
$997$	4.51978	−	16.8680i	0.143143	−	0.534216i	−0.856688	−	0.515835i	$-0.827482\pi$
$997$	4.51978	−	16.8680i	0.143143	−	0.534216i	0.999831	−	0.0183818i	$-0.00585143\pi$
$998$	−0.167661	+	0.625718i	−0.00530721	+	0.0198068i
$999$	−5.71790	+	9.90370i	−0.180906	+	0.313339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.u.b.103.4	yes	16
3.2	odd	2		630.2.bv.b.523.1		16
5.2	odd	4		210.2.u.a.187.2	yes	16
5.3	odd	4		1050.2.bc.h.607.4		16
5.4	even	2		1050.2.bc.g.943.1		16
7.2	even	3		1470.2.m.e.1273.5		16
7.3	odd	6		210.2.u.a.73.2	✓	16
7.5	odd	6		1470.2.m.d.1273.8		16
15.2	even	4		630.2.bv.a.397.3		16
21.17	even	6		630.2.bv.a.73.3		16
35.2	odd	12		1470.2.m.d.97.8		16
35.3	even	12		1050.2.bc.g.157.1		16
35.12	even	12		1470.2.m.e.97.5		16
35.17	even	12	inner	210.2.u.b.157.4	yes	16
35.24	odd	6		1050.2.bc.h.493.4		16
105.17	odd	12		630.2.bv.b.577.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.2	✓	16	7.3	odd	6
210.2.u.a.187.2	yes	16	5.2	odd	4
210.2.u.b.103.4	yes	16	1.1	even	1	trivial
210.2.u.b.157.4	yes	16	35.17	even	12	inner
630.2.bv.a.73.3		16	21.17	even	6
630.2.bv.a.397.3		16	15.2	even	4
630.2.bv.b.523.1		16	3.2	odd	2
630.2.bv.b.577.1		16	105.17	odd	12
1050.2.bc.g.157.1		16	35.3	even	12
1050.2.bc.g.943.1		16	5.4	even	2
1050.2.bc.h.493.4		16	35.24	odd	6
1050.2.bc.h.607.4		16	5.3	odd	4
1470.2.m.d.97.8		16	35.2	odd	12
1470.2.m.d.1273.8		16	7.5	odd	6
1470.2.m.e.97.5		16	35.12	even	12
1470.2.m.e.1273.5		16	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.14315 - 0.637899i) q^{5} -1.00000i q^{6} +(0.153213 + 2.64131i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.14315 - 0.637899i) q^{5} -1.00000i q^{6} +(0.153213 + 2.64131i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.17085 + 1.90502i) q^{10} +(2.27722 + 3.94427i) q^{11} +(0.965926 - 0.258819i) q^{12} +(1.77772 - 1.77772i) q^{13} +(-2.51166 + 0.831614i) q^{14} +(-2.23522 + 0.0614757i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.06747 + 3.98386i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(1.88956 - 3.27281i) q^{19} +(-1.53707 + 1.62401i) q^{20} +(0.535629 - 2.59097i) q^{21} +(-3.22048 + 3.22048i) q^{22} +(-7.77857 + 2.08426i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.18617 - 2.73423i) q^{25} +(2.17725 + 1.25704i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.45334 - 2.21084i) q^{28} -1.55563i q^{29} +(-0.637899 - 2.14315i) q^{30} +(3.37208 - 1.94687i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.17878 - 4.39926i) q^{33} -4.12440 q^{34} +(2.01325 + 5.56299i) q^{35} -1.00000 q^{36} +(-2.95980 - 11.0461i) q^{37} +(3.65035 + 0.978107i) q^{38} +(-2.17725 + 1.25704i) q^{39} +(-1.96650 - 1.06437i) q^{40} -11.3796i q^{41} +(2.64131 - 0.153213i) q^{42} +(0.367260 + 0.367260i) q^{43} +(-3.94427 - 2.27722i) q^{44} +(2.17497 + 0.519137i) q^{45} +(-4.02648 - 6.97408i) q^{46} +(4.87829 - 1.30713i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-6.95305 + 0.809365i) q^{49} +(3.72452 + 3.33586i) q^{50} +(2.06220 - 3.57183i) q^{51} +(-0.650691 + 2.42841i) q^{52} +(-2.18307 + 8.14732i) q^{53} +(0.500000 - 0.866025i) q^{54} +(7.39647 + 7.00051i) q^{55} +(1.75935 - 1.97603i) q^{56} +(-2.67224 + 2.67224i) q^{57} +(1.50262 - 0.402626i) q^{58} +(-0.221511 - 0.383668i) q^{59} +(1.90502 - 1.17085i) q^{60} +(7.09442 + 4.09597i) q^{61} +(2.75329 + 2.75329i) q^{62} +(-1.18797 + 2.36405i) q^{63} +1.00000i q^{64} +(2.67591 - 4.94392i) q^{65} +(3.94427 - 2.27722i) q^{66} +(-8.99808 - 2.41103i) q^{67} +(-1.06747 - 3.98386i) q^{68} +8.05297 q^{69} +(-4.85237 + 3.38446i) q^{70} -6.68403 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-4.20080 - 1.12560i) q^{73} +(9.90370 - 5.71790i) q^{74} +(-4.75120 + 1.55760i) q^{75} +3.77912i q^{76} +(-10.0691 + 6.61917i) q^{77} +(-1.77772 - 1.77772i) q^{78} +(-4.08283 - 2.35722i) q^{79} +(0.519137 - 2.17497i) q^{80} +(0.500000 + 0.866025i) q^{81} +(10.9919 - 2.94527i) q^{82} +(-3.21718 + 3.21718i) q^{83} +(0.831614 + 2.51166i) q^{84} +(0.253550 + 9.21894i) q^{85} +(-0.259692 + 0.449799i) q^{86} +(-0.402626 + 1.50262i) q^{87} +(1.17878 - 4.39926i) q^{88} +(3.02425 - 5.23816i) q^{89} +(0.0614757 + 2.23522i) q^{90} +(4.96788 + 4.42314i) q^{91} +(5.69431 - 5.69431i) q^{92} +(-3.76106 + 1.00777i) q^{93} +(2.52519 + 4.37376i) q^{94} +(1.96188 - 8.21947i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(0.462652 + 0.462652i) q^{97} +(-2.58137 - 6.50665i) q^{98} +4.55445i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 - 4 * q^7	\( 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28} - 4 q^{30} - 24 q^{31} + 4 q^{33} - 16 q^{34} - 44 q^{35} - 16 q^{36} - 8 q^{37} - 20 q^{38} + 12 q^{39} + 8 q^{42} - 24 q^{43} - 4 q^{45} - 4 q^{46} - 52 q^{49} + 8 q^{51} + 8 q^{52} - 28 q^{53} + 8 q^{54} + 56 q^{55} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} + 16 q^{65} - 84 q^{67} + 12 q^{68} + 8 q^{69} + 4 q^{70} - 32 q^{71} + 16 q^{73} + 24 q^{74} - 24 q^{75} + 44 q^{77} - 16 q^{78} - 12 q^{79} + 12 q^{80} + 8 q^{81} + 36 q^{82} + 16 q^{83} - 4 q^{84} + 8 q^{85} - 8 q^{86} + 48 q^{87} - 4 q^{88} + 16 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 8 q^{94} + 72 q^{95} - 44 q^{97} + 24 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

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